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

Suppose $$h(t) is $$the height above the ground, in feet, of a rocket $$t$$ seconds after launching. If $$h(0) = 200$$, what does this mean?

Accepted Answer

The rocket is 200 feet above the ground at launch.

Question 3

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4)\}$$

Question 4

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

Accepted Answer

$$(-\infty, 7]$$

Question 5

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

Accepted Answer

$$[2, \infty)$$

Question 6

Which of the following is an even function?

Accepted Answer

$$f(x) = x^2$

Question 7

Which of the following is an odd function?

Accepted Answer

$$f(x) = x^3$

Question 8

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

Accepted Answer

$$14$$

Question 9

A phone company charges an initial home hookup fee of $$120, and increases at a rate of 8$ for every minute talked. Which equation models the total charge C$ after t$ minutes?

Accepted Answer

$$C = 8t + 120$$

Question 10

Terry is running on a track. His elevation $$E(t) in $$feet after $$t$$ seconds is given by $$E(t) = 1000 - 20t. $$What does the slope of this function represent?

Accepted Answer

Terry's elevation is decreasing by 20 feet per second.

Question 11

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

Accepted Answer

$$y = -\frac{1}{2}x + 3.5$$

Question 12

If $$f(x) = x^2$ is reflected over the x$-axis and then shifted up by 3 units, what is the new function?

Accepted Answer

$$f(x) = -x^2$ + 3$$

Question 13

Given $$f(x) = \sqrt{7 - x}$$ and $$g(x) = x^2$ - 2$$, find $$f(g(1)).$$

Accepted Answer

$$2$$

Question 14

Which transformation will shift the graph of $$f(x)$$ vertically upward by 4 units?

Accepted Answer

$$f(x) + 4$$

Question 15

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

Accepted Answer

$$(-\infty, \infty)$$

Question 16

A population in a park was measured to be 1200 in 1990 and 6600 in 2000. Assuming linear growth, what is the average rate of change per year?

Accepted Answer

$$540$$

Question 17

Which of the following best describes the range of $$f(x) = \sqrt{7 - x}$$?

Accepted Answer

$$[0, \infty)$$

Question 18

Given the piecewise function $$f(x) = \begin{cases} -x^2$ + 5 & x \leq 2 \ x + 2 & x \u003e 2 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$1$$

Question 19

If $$f(x) = x^2$ is vertically stretched by a factor of 3 and then shifted to the left by 2 units, what is the new function?

Accepted Answer

$$f(x) = 3(x + 2)^2$

Precalculus Exam 1 Review: Functions, Graphs, and Applications

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