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 $f(2)$ .
$f(x) = \begin{cases} x + 3 & \text{if } x < 5 \\ 3x & \text{if } x \ge 5 \end{cases}$ . 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. $-x - 3$
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
How does the graph of $y = f(4x)$ compare with the graph of $y = f(x)$ ?
1. It is squeezed toward the y-axis: horizontal compression by a factor of 4
2. It is pulled away from the y-axis: horizontal stretch by a factor of 4
3. It is stretched vertically by a factor of 4
How does the graph of $y = f(5x)$ compare with the graph of $y = f(x)$ ?
1. It is squeezed toward the y-axis: horizontal compression by a factor of 5
2. It is pulled away from the y-axis: horizontal stretch by a factor of 5
3. It is stretched vertically by a factor of 5
How does the graph of $y = f(3x)$ compare with the graph of $y = f(x)$ ?
1. It is squeezed toward the y-axis: horizontal compression by a factor of 3
2. It is pulled away from the y-axis: horizontal stretch by a factor of 3
3. It is stretched vertically by a factor of 3
How does the graph of $y = f(2x)$ compare with the graph of $y = f(x)$ ?
1. It is squeezed toward the y-axis: horizontal compression by a factor of 2
2. It is pulled away from the y-axis: horizontal stretch by a factor of 2
3. It is stretched vertically by a factor of 2
$f(x) = 8x^3 - 9x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 9x^3 - 2x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^3 - 1x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^3 - 1x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 9x^3 - 3x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^3 - 4x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^3 - 5x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^3 - 9x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^3 - 7x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^3 - 6x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^3 - 3x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^3 - 7x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^3 - 2x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^3 - 7x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^3 - 4x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^3 - 1x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^3 - 8x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^3 - 3x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^3 - 5x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^3 - 4x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^3 - 1x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 9x^3 - 8x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^3 - 4x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^3 - 7x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 9x^3 - 4x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^3 - 8x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^3 - 5x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^3 - 2x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^3 - 2x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^3 - 1x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^3 - 6x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^3 - 5x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^3 - 5x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^3 - 6x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^3 - 4x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^3 - 1x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^3 - 9x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^3 - 9x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^3 - 9x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^3 - 6x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^3 - 2x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^3 - 9x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^3 - 7x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^3 - 4x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^3 - 3x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^3 - 6x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^3 - 1x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 9x^3 - 6x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^3 - 3x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^3 - 8x$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^4 - 8x^2 + 7$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 1x^2 + 9$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^4 - 2x^2 + 8$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^4 - 8x^2 + 7$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 5x^2 + 8$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^4 - 1x^2 + 7$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^4 - 4x^2 + 9$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^4 - 9x^2 + 9$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^4 - 9x^2 + 3$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^4 - 4x^2 + 2$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 9x^4 - 7x^2 + 6$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 9x^2 + 9$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^4 - 6x^2 + 7$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^4 - 7x^2 + 2$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^4 - 3x^2 + 1$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 9x^2 + 6$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^4 - 7x^2 + 6$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^4 - 6x^2 + 8$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^4 - 5x^2 + 1$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^4 - 1x^2 + 8$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^4 - 7x^2 + 9$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^4 - 3x^2 + 3$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 9x^4 - 1x^2 + 1$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 9x^4 - 8x^2 + 2$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^4 - 6x^2 + 1$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^4 - 4x^2 + 8$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^4 - 8x^2 + 6$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^4 - 3x^2 + 2$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^4 - 1x^2 + 8$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 6x^2 + 1$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 6x^2 + 7$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^4 - 5x^2 + 6$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 6x^4 - 6x^2 + 2$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^4 - 7x^2 + 6$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 2x^2 + 2$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^4 - 5x^2 + 3$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 1x^2 + 8$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 9x^2 + 8$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^4 - 4x^2 + 9$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 3x^4 - 3x^2 + 3$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 3x^2 + 2$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^4 - 2x^2 + 7$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 5x^2 + 2$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^4 - 6x^2 + 3$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^4 - 1x^2 + 6$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x^4 - 8x^2 + 4$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 7x^4 - 5x^2 + 6$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 4x^4 - 6x^2 + 5$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 8x^4 - 4x^2 + 1$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 5x^4 - 8x^2 + 4$ . Is $f$ even, odd, or neither?
1. Even
2. Odd
3. Neither
$f(x) = 2x + 2$ and $g(x) = x^2 - 2$ . Find $f(g(3))$ .
$f(x) = 6x + 6$ and $g(x) = x + 5$ . Write $f(g(x))$ .
$g(1) = 5$ , $g(5) = 7$ , $f(1) = 7$ and $f(5) = 1$ . Find $f(g(1))$ .
$f(x) = 7x + 9$ . 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 $f^{-1}$ .

Answers

$21$
$28$
$(2, -1)$
$15$
$4$
$7 - x$
$y = \left(x - 1\right)^{2} - 3$
$\left(x - 1\right)^{2} - 6$
$y = f(x) + 3$ → 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
It is squeezed toward the y-axis: horizontal compression by a factor of 4
Odd
Even
$16$
$6 x + 36$
$1$
$\frac{x}{7} - \frac{9}{7}$
$2$
$(7, 2)$