Review of Functions

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Show your work for each problem.

1.
If $f(x) = 3x + 2$ , what is $f(4)$ ?
1. a)10
2. b)12
3. c)9
4. d)14
2.
If $g(x) = x^2 - 1$ , find $g(3)$ .
3.
Which graph passes the vertical line test?
1. a)A horizontal parabola
2. b)A circle
3. c)A parabola opening upward
4. d)A figure-eight
4.
If $f(x) = 2x - 5$ , find $f(-3)$ .
5.
If $h(x) = |x - 3|$ , find $h(1)$ .
6.
What is the domain of $f(x) = \sqrt{x + 4}$ ?
1. a) $x \geq -4$
2. b) $x \leq -4$
3. c) $x \geq 4$
4. d)All real numbers
7.
Given $f(x) = x + 2$ and $g(x) = 3x$ , find $(f + g)(4)$ .
8.
Given $f(x) = x^2$ and $g(x) = x + 1$ , find $(f \circ g)(2)$ .
9.
Given $f(x) = 2x$ and $g(x) = x - 3$ , find $(g \circ f)(5)$ .
10.
If $f(x) = \frac{1}{x - 2}$ , what value is NOT in the domain?
1. a) $x = -2$
2. b) $x = 1$
3. c) $x = 2$
4. d) $x = 0$
11.
Given $f(x) = x + 5$ and $g(x) = 2x$ , find $(f \cdot g)(3)$ .
12.
Evaluate the piecewise function at $x = -1$ :
$f(x) = \begin{cases} x + 4 & \text{if } x < 0 \\ 2x & \text{if } x \geq 0 \end{cases}$
13.
What is the range of $f(x) = x^2 + 1$ ?
1. a)All real numbers
2. b) $y > 1$
3. c) $y \geq 1$
4. d) $y \geq 0$
14.
Given $f(x) = x^2 - 4$ and $g(x) = x + 2$ , find $\left(\frac{f}{g}\right)(3)$ .
15.
If $f(x) = 3x - 1$ and $(f \circ f)(a) = 23$ , find $a$ .
16.
Find the domain of $f(x) = \frac{\sqrt{x}}{x - 4}$ .
17.
If $f(x) = x + 3$ and $g(x) = x^2$ , which expression equals $(f \circ g)(x)$ ?
1. a) $x^2 + 6x + 9$
2. b) $x^2 + 3x$
3. c) $x^2 + 3$
4. d) $(x + 3)^2$
18.
If $f(x) = \frac{x + 1}{x - 1}$ , find $f(f(2))$ .