Practice sheet

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

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$f(x) = 2x + 2$ 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 $f(g(1))$ .
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
$f(x) = 7x + 9$ . 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 $f^{-1}$ .
The graph of $y = 3\cdot 4^x + 7$ has a horizontal asymptote $y = c$ . What is $c$ ?
The graph of $y = \log_{ 4 }(x - 6) + 1$ has a vertical asymptote $x = c$ . What is $c$ ?
Draw the graph of $y = 1 \cdot 2^x + 3$ : place two points and the asymptote.

Answers

$16$
$6 x + 36$
$1$
$y = \left(x - 1\right)^{2} - 3$
$\left(x - 1\right)^{2} - 6$
$y = f(x) + 3$ → 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
$\frac{x}{7} - \frac{9}{7}$
$2$
$(7, 2)$
$7$
$6$
$y = 2^{x} + 3$