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A table pairs inputs $x$ with outputs $y$ : $(x, y) = (5, 1), (5, 2), (9, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 5 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (4, 1), (4, 2), (6, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 4 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 1), (2, 2), (8, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 2 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 1), (3, 2), (7, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 3 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (4, 1), (4, 2), (9, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 4 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (5, 1), (5, 2), (6, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 5 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (4, 1), (4, 2), (7, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 4 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 1), (2, 2), (9, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 2 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 1), (1, 2), (9, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 1 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (5, 1), (5, 2), (8, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 5 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (5, 1), (5, 2), (7, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 5 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 1), (1, 2), (8, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 1 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 1), (3, 2), (6, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 3 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 1), (3, 2), (8, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 3 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 1), (1, 2), (6, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 1 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 1), (2, 2), (6, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 2 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 1), (1, 2), (7, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 1 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 1), (2, 2), (7, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 2 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 1), (3, 2), (9, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 3 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (4, 1), (4, 2), (8, 3)$ . Is $y$ a function of $x$ ?
1. No: the input 4 has two different outputs
2. Yes: every input has an output
3. Yes: the outputs are all different
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 5), (5, 5), (9, 5)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 5 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 3), (5, 3), (9, 3)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 3 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 6), (6, 6), (7, 6)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 6 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 3), (6, 3), (7, 3)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 3 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 7), (5, 7), (8, 7)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 7 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 8), (6, 8), (7, 8)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 8 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 4), (5, 4), (8, 4)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 4 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 3), (5, 3), (7, 3)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 3 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 3), (5, 3), (9, 3)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 3 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 4), (6, 4), (7, 4)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 4 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 1), (6, 1), (7, 1)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 1 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 7), (4, 7), (9, 7)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 7 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 3), (4, 3), (8, 3)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 3 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 4), (5, 4), (7, 4)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 4 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 4), (4, 4), (8, 4)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 4 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 5), (6, 5), (9, 5)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 5 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 8), (6, 8), (8, 8)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 8 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 4), (4, 4), (7, 4)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 4 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 7), (4, 7), (7, 7)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 7 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 7), (5, 7), (7, 7)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 7 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 6), (4, 6), (9, 6)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 6 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 8), (4, 8), (9, 8)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 8 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 9), (6, 9), (9, 9)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 9 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 8), (6, 8), (9, 8)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 8 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 1), (5, 1), (9, 1)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 1 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 2), (5, 2), (9, 2)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 2 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 6), (6, 6), (9, 6)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 6 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 7), (4, 7), (7, 7)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 7 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 2), (4, 2), (7, 2)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 2 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 8), (4, 8), (8, 8)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 8 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 9), (5, 9), (9, 9)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 9 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 1), (6, 1), (7, 1)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 1 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 3), (5, 3), (8, 3)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 3 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 7), (6, 7), (9, 7)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 7 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 1), (6, 1), (9, 1)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 1 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 2), (4, 2), (8, 2)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 2 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 8), (6, 8), (8, 8)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 8 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 2), (4, 2), (9, 2)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 2 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 5), (5, 5), (7, 5)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 5 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 8), (4, 8), (9, 8)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 8 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 6), (4, 6), (8, 6)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 6 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 2), (5, 2), (9, 2)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 2 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 4), (5, 4), (9, 4)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 4 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 8), (5, 8), (7, 8)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 8 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (2, 3), (6, 3), (9, 3)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 3 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 4), (6, 4), (7, 4)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 4 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 4), (4, 4), (9, 4)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 4 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 3), (4, 3), (7, 3)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 3 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (1, 2), (5, 2), (7, 2)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 2 repeats
3. No: a function needs a formula
A table pairs inputs $x$ with outputs $y$ : $(x, y) = (3, 2), (5, 2), (7, 2)$ . Is $y$ a function of $x$ ?
1. Yes: each input has exactly one output
2. No: the output 2 repeats
3. No: a function needs a formula
A function's rule: multiply the input by 6, then add 6. Which input gives the output 24?
$f(x) = 2x^2 + 3$ . Find $f(-3)$ .
$f(x) = x^2 + 3$ . Find $f(2 + 3)$ .
Here is the graph of $y = f(x)$ . Tap the point of the graph that shows $f(2)$ .
What is the domain of $f(x) = \sqrt{x - 9}$ ? Give it as an interval.
What is the domain of $f(x) = \dfrac{ 9 }{x - 6}$ ? Give it as an interval or a union of intervals.
What is the range of $f(x) = (x - 5)^2 + 9$ ? Give it as an interval.
Find the average rate of change of $f(x) = 3x^2$ from $x = 0$ to $x = 6$ .
$f(x) = -(x - 5)^2 + 8$ . On which interval is $f$ increasing?
1. $(-\infty, 5)$
2. $(5, \infty)$
3. $(-\infty, 8)$
$f(x) = -(x - 1)^2 + 7$ . On which interval is $f$ increasing?
1. $(-\infty, 1)$
2. $(1, \infty)$
3. $(-\infty, 7)$
$f(x) = -(x - 3)^2 + 2$ . On which interval is $f$ increasing?
1. $(-\infty, 3)$
2. $(3, \infty)$
3. $(-\infty, 2)$
$f(x) = -(x - 1)^2 + 2$ . On which interval is $f$ increasing?
1. $(-\infty, 1)$
2. $(1, \infty)$
3. $(-\infty, 2)$
$f(x) = -(x - 4)^2 + 8$ . On which interval is $f$ increasing?
1. $(-\infty, 4)$
2. $(4, \infty)$
3. $(-\infty, 8)$
$f(x) = -(x - 3)^2 + 9$ . On which interval is $f$ increasing?
1. $(-\infty, 3)$
2. $(3, \infty)$
3. $(-\infty, 9)$
$f(x) = -(x - 4)^2 + 7$ . On which interval is $f$ increasing?
1. $(-\infty, 4)$
2. $(4, \infty)$
3. $(-\infty, 7)$
$f(x) = -(x - 3)^2 + 6$ . On which interval is $f$ increasing?
1. $(-\infty, 3)$
2. $(3, \infty)$
3. $(-\infty, 6)$
$f(x) = -(x - 4)^2 + 2$ . On which interval is $f$ increasing?
1. $(-\infty, 4)$
2. $(4, \infty)$
3. $(-\infty, 2)$
$f(x) = -(x - 4)^2 + 3$ . On which interval is $f$ increasing?
1. $(-\infty, 4)$
2. $(4, \infty)$
3. $(-\infty, 3)$
$f(x) = -(x - 2)^2 + 3$ . On which interval is $f$ increasing?
1. $(-\infty, 2)$
2. $(2, \infty)$
3. $(-\infty, 3)$
$f(x) = -(x - 4)^2 + 1$ . On which interval is $f$ increasing?
1. $(-\infty, 4)$
2. $(4, \infty)$
3. $(-\infty, 1)$
$f(x) = -(x - 5)^2 + 7$ . On which interval is $f$ increasing?
1. $(-\infty, 5)$
2. $(5, \infty)$
3. $(-\infty, 7)$
$f(x) = -(x - 3)^2 + 7$ . On which interval is $f$ increasing?
1. $(-\infty, 3)$
2. $(3, \infty)$
3. $(-\infty, 7)$
$f(x) = -(x - 4)^2 + 6$ . On which interval is $f$ increasing?
1. $(-\infty, 4)$
2. $(4, \infty)$
3. $(-\infty, 6)$
$f(x) = -(x - 1)^2 + 5$ . On which interval is $f$ increasing?
1. $(-\infty, 1)$
2. $(1, \infty)$
3. $(-\infty, 5)$
$f(x) = -(x - 3)^2 + 1$ . On which interval is $f$ increasing?
1. $(-\infty, 3)$
2. $(3, \infty)$
3. $(-\infty, 1)$
$f(x) = -(x - 2)^2 + 9$ . On which interval is $f$ increasing?
1. $(-\infty, 2)$
2. $(2, \infty)$
3. $(-\infty, 9)$
$f(x) = -(x - 3)^2 + 8$ . On which interval is $f$ increasing?
1. $(-\infty, 3)$
2. $(3, \infty)$
3. $(-\infty, 8)$
$f(x) = -(x - 5)^2 + 6$ . On which interval is $f$ increasing?
1. $(-\infty, 5)$
2. $(5, \infty)$
3. $(-\infty, 6)$
$f(x) = -(x - 1)^2 + 9$ . On which interval is $f$ increasing?
1. $(-\infty, 1)$
2. $(1, \infty)$
3. $(-\infty, 9)$
$f(x) = -(x - 4)^2 + 9$ . On which interval is $f$ increasing?
1. $(-\infty, 4)$
2. $(4, \infty)$
3. $(-\infty, 9)$
$f(x) = -(x - 2)^2 + 8$ . On which interval is $f$ increasing?
1. $(-\infty, 2)$
2. $(2, \infty)$
3. $(-\infty, 8)$
$f(x) = -(x - 5)^2 + 2$ . On which interval is $f$ increasing?
1. $(-\infty, 5)$
2. $(5, \infty)$
3. $(-\infty, 2)$
$f(x) = -(x - 3)^2 + 5$ . On which interval is $f$ increasing?
1. $(-\infty, 3)$
2. $(3, \infty)$
3. $(-\infty, 5)$
$f(x) = -(x - 2)^2 + 5$ . On which interval is $f$ increasing?
1. $(-\infty, 2)$
2. $(2, \infty)$
3. $(-\infty, 5)$
$f(x) = -(x - 1)^2 + 4$ . On which interval is $f$ increasing?
1. $(-\infty, 1)$
2. $(1, \infty)$
3. $(-\infty, 4)$
$f(x) = -(x - 1)^2 + 6$ . On which interval is $f$ increasing?
1. $(-\infty, 1)$
2. $(1, \infty)$
3. $(-\infty, 6)$
$f(x) = -(x - 5)^2 + 9$ . On which interval is $f$ increasing?
1. $(-\infty, 5)$
2. $(5, \infty)$
3. $(-\infty, 9)$
$f(x) = -(x - 4)^2 + 5$ . On which interval is $f$ increasing?
1. $(-\infty, 4)$
2. $(4, \infty)$
3. $(-\infty, 5)$
$f(x) = -(x - 2)^2 + 1$ . On which interval is $f$ increasing?
1. $(-\infty, 2)$
2. $(2, \infty)$
3. $(-\infty, 1)$
$f(x) = -(x - 2)^2 + 7$ . On which interval is $f$ increasing?
1. $(-\infty, 2)$
2. $(2, \infty)$
3. $(-\infty, 7)$
$f(x) = -(x - 2)^2 + 6$ . On which interval is $f$ increasing?
1. $(-\infty, 2)$
2. $(2, \infty)$
3. $(-\infty, 6)$
$f(x) = -(x - 1)^2 + 8$ . On which interval is $f$ increasing?
1. $(-\infty, 1)$
2. $(1, \infty)$
3. $(-\infty, 8)$
$f(x) = -(x - 5)^2 + 4$ . On which interval is $f$ increasing?
1. $(-\infty, 5)$
2. $(5, \infty)$
3. $(-\infty, 4)$
$f(x) = -(x - 5)^2 + 1$ . On which interval is $f$ increasing?
1. $(-\infty, 5)$
2. $(5, \infty)$
3. $(-\infty, 1)$
$f(x) = -(x - 3)^2 + 4$ . On which interval is $f$ increasing?
1. $(-\infty, 3)$
2. $(3, \infty)$
3. $(-\infty, 4)$
$f(x) = -(x - 2)^2 + 4$ . On which interval is $f$ increasing?
1. $(-\infty, 2)$
2. $(2, \infty)$
3. $(-\infty, 4)$
$f(x) = -(x - 5)^2 + 3$ . On which interval is $f$ increasing?
1. $(-\infty, 5)$
2. $(5, \infty)$
3. $(-\infty, 3)$
$f(x) = -(x - 1)^2 + 3$ . On which interval is $f$ increasing?
1. $(-\infty, 1)$
2. $(1, \infty)$
3. $(-\infty, 3)$
A tank holds 16 liters at time 0 and $61$ liters after 5 minutes. What is the average rate of change of the volume, in liters per minute?
Draw the graph of $y = (x - 1)^2 - 3$ : place the vertex and one more point.
The graph of $y = x^2$ is moved 1 units to the right and 6 units down. Write the equation of the new graph.
Match each equation with what it does to the graph of $y = f(x)$ .
1. $y = f(x) + 3$
2. $y = f(x - 3)$
3. $y = -f(x)$
4. $y = f(-x)$
1. moves it up 3 units
2. moves it 3 units to the right
3. reflects it across the x-axis
4. reflects it across the y-axis
Match each equation with what it does to the graph of $y = f(x)$ .
1. $y = f(x) + 5$
2. $y = f(x - 5)$
3. $y = -f(x)$
4. $y = f(-x)$
1. moves it up 5 units
2. moves it 5 units to the right
3. reflects it across the x-axis
4. reflects it across the y-axis
Match each equation with what it does to the graph of $y = f(x)$ .
1. $y = f(x) + 4$
2. $y = f(x - 4)$
3. $y = -f(x)$
4. $y = f(-x)$
1. moves it up 4 units
2. moves it 4 units to the right
3. reflects it across the x-axis
4. reflects it across the y-axis
Match each equation with what it does to the graph of $y = f(x)$ .
1. $y = f(x) + 2$
2. $y = f(x - 2)$
3. $y = -f(x)$
4. $y = f(-x)$
1. moves it up 2 units
2. moves it 2 units to the right
3. reflects it across the x-axis
4. reflects it across the y-axis
$a_1 = 3$ and $a_{n+1} = 2a_n - 7$ . Find $a_3$ .
Write a formula for $a_n$ , starting at $n = 1$ : $1,6, 11, 16, \dots$
$a_n = n^2 + 5$ . Complete the table.
An arithmetic sequence has $a_1 = 14$ and common difference 2. Find $a_{ 43 }$ .
In an arithmetic sequence, $a_{ 4 } = 28$ and $a_{ 9 } = 68$ . Find the common difference.
What kind of sequence is $3, 6, 12, 24, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $1, 2, 4, 8, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $3, 12, 48, 192, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $3, 9, 27, 81, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $4, 8, 16, 32, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $2, 8, 32, 128, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $4, 12, 36, 108, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $1, 4, 16, 64, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $5, 20, 80, 320, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $2, 4, 8, 16, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $5, 15, 45, 135, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $5, 10, 20, 40, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $2, 6, 18, 54, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $4, 16, 64, 256, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $1, 3, 9, 27, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
A geometric sequence has $a_1 = 3$ and ratio 3. Find $a_{ 4 }$ .
Find the common ratio of the geometric sequence $8, 32, 128, \dots$
Write a formula for $a_n$ , starting at $n = 1$ : $2, 8, 32, \dots$

Answers

No: the input 5 has two different outputs
Yes: each input has exactly one output
$3$
$21$
$28$
$(2, -1)$
$[9, \infty)$
$(-\infty, 6) \cup (6, \infty)$
$[9, \infty)$
$18$
$(-\infty, 5)$
$9$
$y = \left(x - 1\right)^{2} - 3$
$\left(x - 1\right)^{2} - 6$
$y = f(x) + 3$ → moves it up 3 units · $y = f(x - 3)$ → moves it 3 units to the right · $y = -f(x)$ → reflects it across the x-axis · $y = f(-x)$ → reflects it across the y-axis
$-9$
$5 n - 4$
$6, 9, 14, 21$
$98$
$8$
Geometric, with ratio 2
$81$
$4$
$2 \cdot 4^{n - 1}$