Practice sheet

Fresh questions from the whole chapter, to do on paper.

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$f(x) = 2x^2 + 3$ . 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 $f(2)$ .
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?
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.
$f(x) = \begin{cases} x + 3 & \text{if } x < 5 \\ 3x & \text{if } x \ge 5 \end{cases}$ . Find $f(5)$ .
$f(x) = \begin{cases} x + 4 & \text{if } x < 8 \\ 4x & \text{if } x \ge 8 \end{cases}$ . Find $f(0)$ .
For $x < 7$ , which expression is equal to $|x - 7|$ ?
1. $7 - x$
2. $x - 7$
3. $-x - 7$
For $x < 5$ , which expression is equal to $|x - 5|$ ?
1. $5 - x$
2. $x - 5$
3. $-x - 5$
For $x < 1$ , which expression is equal to $|x - 1|$ ?
1. $1 - x$
2. $x - 1$
3. $-x - 1$
For $x < 9$ , which expression is equal to $|x - 9|$ ?
1. $9 - x$
2. $x - 9$
3. $-x - 9$
For $x < 8$ , which expression is equal to $|x - 8|$ ?
1. $8 - x$
2. $x - 8$
3. $-x - 8$
For $x < 6$ , which expression is equal to $|x - 6|$ ?
1. $6 - x$
2. $x - 6$
3. $-x - 6$
For $x < 4$ , which expression is equal to $|x - 4|$ ?
1. $4 - x$
2. $x - 4$
3. $-x - 4$
For $x < 2$ , which expression is equal to $|x - 2|$ ?
1. $2 - x$
2. $x - 2$
3. $-x - 2$
For $x < 3$ , which expression is equal to $|x - 3|$ ?
1. $3 - x$
2. $x - 3$
3. $-x - 3$
$f(x) = 7x + 9$ . Find $f^{-1}(x)$ .
$f(x) = 2x + 6$ . Find $f^{-1}(10)$ .
The point $(2, 7)$ is on the graph of $f$ . Tap the point that must be on the graph of $f^{-1}$ .
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.

Answers

$21$
$28$
$(2, -1)$
$18$
$(-\infty, 5)$
$9$
$[9, \infty)$
$(-\infty, 6) \cup (6, \infty)$
$[9, \infty)$
$15$
$4$
$7 - x$
$\frac{x}{7} - \frac{9}{7}$
$2$
$(7, 2)$
$y = \left(x - 1\right)^{2} - 3$
$\left(x - 1\right)^{2} - 6$
$y = f(x) + 3$ → 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
$-9$
$5 n - 4$
$6, 9, 14, 21$