Domain and Range

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Show your work for each problem.

1.
What does the domain of a function represent?
1. a)The highest point on the graph
2. b)All possible output values (y-values)
3. c)The slope of the function
4. d)All possible input values (x-values)
2.
A graph starts at a solid dot at $x = -2$ and ends at a solid dot at $x = 6$ . What is the domain in interval notation?
1. a) $(-2, 6)$
2. b) $[-2, 6]$
3. c) $(-2, 6]$
4. d) $[-2, 6)$
3.
A parabola has its vertex at $(0, 3)$ and opens upward. What is the minimum value of the range?
4.
For $f(x) = \frac{1}{x}$ , what value of $x$ is NOT in the domain?
5.
Which bracket notation should you always use with infinity ( $\infty$ )?
1. a)Parenthesis $( )$
2. b)Curly bracket $\{ \}$
3. c)Either one works
4. d)Square bracket $[ ]$
6.
Find the domain of $f(x) = \frac{1}{x-5}$
7.
Find the domain of $g(x) = \sqrt{x - 4}$
8.
The range of a function is $[-2, \infty)$ . What is the minimum y-value the function can produce?
9.
What is the domain of $f(x) = x^2 + 3x - 7$ ?
1. a) $(-\infty, 7]$
2. b) $[0, \infty)$
3. c) $[-7, \infty)$
4. d) $(-\infty, \infty)$
10.
Find the domain and range of $f(x) = x^2 + 2$
11.
For $f(x) = \sqrt{x}$ , the range is $[a, \infty)$ . What is $a$ ?
12.
Find the domain of $f(x) = \frac{1}{x^2 - 9}$
13.
What is the domain of $f(x) = \sqrt{2x + 6}$ ?
1. a) $[-6, \infty)$
2. b) $[-3, \infty)$
3. c) $(-\infty, -3]$
4. d) $[3, \infty)$
14.
Find the domain of $h(x) = \frac{\sqrt{x}}{x - 4}$
15.
A parabola opens downward with vertex at $(2, 8)$ . What is the maximum value in its range?
16.
Find the range of $f(x) = -x^2 + 4x + 5$