Question 1

Let $$f(t) be $$the number of ducks in a lake $$t$$ years after 1990. If $$f(0) = 30$$ and $$f(10) = 40$$, what does $$f(0)$$ represent in this context?

Accepted Answer

The number of ducks in the lake in 1990.

Question 2

A rocket launches and its height above the ground $$h(t) (in $$feet) after $$t$$ seconds is given by $$h(t) = 200 + 50t. $$What is the height of the rocket 4 seconds after launch?

Accepted Answer

$$h(4) = 400$$ feet

Question 3

Which of the following is a function?

Accepted Answer

A relation where each input has exactly one output.

Question 4

Find the domain of the function $$f(x) = \sqrt{7 - x}.$$

Accepted Answer

$$(-\infty, 7]$$

Question 5

Given the piecewise function $$f(x) = \begin{cases} -x^2$ & x \leq 2 \ x+2 & x \u003e 2 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$-4$$

Question 6

Find the average rate of change of $$f(x) = 2x^2$ - 3x on $$the interval $$[-2, 5].$$

Accepted Answer

$$14$$

Question 7

If $$g(x) = \sqrt{x-2}$$, what is the domain of $$g(x)$$?

Accepted Answer

$$[2, \infty)$$

Question 8

A phone company charges an initial fee of $$12 and 0.15 $$per minute for calls. Which function models the total cost $$C$$ for $$t$$ minutes?

Accepted Answer

$$C(t) = 12 + 0.15t$$

Question 9

Which transformation describes $$g(x) = 2f(x-3) + 1$$ relative to $$f(x)$$?

Accepted Answer

Shift right 3, stretch vertically by 2, shift up 1

Question 10

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 1$$, find $$(f \circ g)(2).$$

Accepted Answer

$$f(g(2)) = f(5) = 25 - 4 = 21$$

Question 11

A population $$P(t) in a $$park was 600 in 1991 and 1200 in 1999. If the population continues to change linearly, what is the formula for $$P(t)$$, where $$t is $$the number of years since 1991?

Accepted Answer

$$P(t) = 600 + 75t$$

Question 12

Given the function $$f(x) = \frac{2x-1}{x+3}$$, what is the domain?

Accepted Answer

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

Question 13

If $$f(x) = |x|$$, which of the following describes its graph?

Accepted Answer

A V-shaped graph opening upwards with vertex at the origin.

Question 14

Find the equation of the line in slope-intercept form passing through $$(-1,4)$$ and $$(3,2).$$

Accepted Answer

$$y = -\frac{1}{2}x + \frac{7}{2}$$

Question 15

A jewelry store's penalty charge is modeled by $$C(t) = 812 + 18t$$, where $$t is $$the number of minutes late. What does the 18 represent?

Accepted Answer

The penalty charge per minute late.

Question 16

Given $$f(x) = x^2$ - 4x + 3$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 17

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

Accepted Answer

$$f(2) + g(2) = 4 + 3 = 7$$

Question 18

Which of the following best describes the transformation $$y = -f(x+2)$$?

Accepted Answer

Reflect $$f(x)$$ over the $$x-$$axis and shift left 2 units.

Question 19

If $$f(x) = \sqrt{x-1}$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 20

A car rental company charges $$C(x) = 40 + 0.25x$$ dollars, where $$x is $$the number of miles driven. What is the cost to drive 100 miles?

Accepted Answer

$$C(100) = 65$$

Precalculus Exam 1 Review: Functions, Graphs, and Transformations

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