Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 2

A postal rate function assigns a price to each letter based on its weight. If $$P(w) is $$the price for a letter weighing $$w$$ ounces (up to 3.5 ounces), what is the domain of $$P(w)$$?

Accepted Answer

$$\{1, 2, 3, 3.5\}$$

Question 3

Which statement about functions is TRUE?

Accepted Answer

The range is the set of possible output values.

Question 4

Given $$f(x) = 2x + 5$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2$$

Question 5

Which of the following graphs passes the Vertical Line Test and represents a function?

Accepted Answer

A parabola opening upwards

Question 6

For the function $$f(x) = \frac{1}{x-3}$$, what is the domain?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 7

A car is purchased for $$22,500 and decreases in value by 3$$,200 per year for the first seven years. Which function best models the value $$V(t)$$ after $$t$$ years, where $$0 \leq t \leq 7$$?

Accepted Answer

$$V(t) = 22,500 - 3,200t$$

Question 8

If $$g(x) = |x-2|$$, what is $$g(-1)$$?

Accepted Answer

$$3$$

Question 9

Which of the following is NOT a function?

Accepted Answer

A mapping where $$x=2$$ maps to both $$y=3$$ and $$y=4$$

Question 10

For the piecewise function $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x+1 & x \geq 0 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$5$$

Question 11

If the graph of a function $$f$$ passes through the points $$(0, 2)$$ and $$(3, 5)$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: none; $$y-$$intercept: $$2$$

Question 12

Which of the following best describes the range of $$f(x) = x^2$ for x$$ \in [-2, 3]$$?

Accepted Answer

$$[0, 9]$$

Question 13

A piecewise function models tax owed by a married person filing separately. If $$T(x) is $$defined as $$T(x) = 0.1x$$ for $$x \leq 10,000$$ and $$T(x) = 1,000 + 0.15(x-10,000)$$ for $$x \u003e 10,000$$, what is $$T(12,000)$$?

Accepted Answer

$$1,300$$

Question 14

Which of the following statements about the difference quotient is correct?

Accepted Answer

It measures the average rate of change of a function over an interval.

Question 15

For the function $$f(x) = \frac{1}{x}$$, which value is NOT in the domain?

Accepted Answer

$$0$$

Question 16

If $$f(x) = x^2$ - 4x + 7$$, what is $$f(3)$$?

Accepted Answer

$$4$$

Question 17

Which scenario is an example of a piecewise-defined function?

Accepted Answer

A tax rate that changes at different income levels

Question 18

If $$f(x) = x^2$ and g(x) = 2x + 1$, what is f(g(2$$))$$?

Accepted Answer

$$25$$

Question 19

Which of the following is the correct interpretation of the dependent variable in a function?

Accepted Answer

It is the output value determined by the input.

Question 20

For the function $$f(x) = \sqrt{9 - x^2$}$$, what is the domain?

Accepted Answer

$$[-3, 3]$$

Basics of Functions and Their Graphs

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