Question 1

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

Accepted Answer

$$\{(1, 4), (2, 5), (3, 6)\}$$

Question 2

Given $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 2(-2)^2$ - 3(-2) + 1 = 8 + 6 + 1 = 15$$

Question 3

What is the domain of $$g(x) = \sqrt{10 - x}$$?

Accepted Answer

$$(-\infty, 10]$$

Question 4

Which of the following graphs passes the vertical line test?

Accepted Answer

A straight line with positive slope

Question 5

Given $$f(x) = |x - 4|$$, what is the absolute minimum value and where does it occur?

Accepted Answer

Absolute minimum is $$0 at$$ $$x = 4$$

Question 6

Which of the following describes the transformation of $$y = \sqrt{x}$$ that is shifted 3 units to the left, reflected across the x-axis, and shifted 5 units up?

Accepted Answer

$$y = -\sqrt{x + 3} + 5$$

Question 7

For the function $$f(x) = x^2$ + x$$, determine whether it is even, odd, or neither.

Accepted Answer

Neither

Question 8

A company’s profit $$P(x) in $$thousands of dollars is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold in hundreds. What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18$$ thousand dollars at $$x = 2$$

Question 9

Find the $$x- $$and $$y-$$intercepts of $$y = 8 + 5x.$$

Accepted Answer

$$x-$$intercept: $$(-\frac{8}{5}, 0)$$, $$y-$$intercept: $$(0, 8)$$

Question 10

Which interval notation represents all real numbers $$x$$ such that $$x \u003e -2$$ and $$x \leq 5$$?

Accepted Answer

$$(-2, 5]$$

Question 11

Suppose $$h(x) = \dfrac{2}{x + 5}. $$What is the domain of $$h(x)$$?

Accepted Answer

$$(-\infty, -5) \cup (-5, \infty)$$

Question 12

If $$f(x) is $$increasing on $$(-\infty, 3)$$ and decreasing on $$(3, \infty)$$, what can you say about $$x = 3$$?

Accepted Answer

$$x = 3 is a $$local maximum$

Question 13

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 14

A population of bacteria doubles every hour and is modeled by $$P(t) = 100 \cdot 2^t$$, where $$t is $$time in hours. What is the range of $$P(t)$$?

Accepted Answer

$$(0, \infty)$$

Question 15

Which transformation will reflect the graph of $$f(x)$$ over the y-axis?

Accepted Answer

$$f(-x)$$

Question 16

Given $$f(x) = (x - 3)^2$, on which interval is f(x$$)$$ decreasing?

Accepted Answer

$$(-\infty, 3)$$

Question 17

A ball is thrown upward and its height in meters after $$t$$ seconds is $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 18

Which of the following is NOT a function?

Accepted Answer

A graph where some vertical lines cross the graph more than once

Question 19

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

Accepted Answer

$$9$$

Study Guide: Relations, Functions, and Graphs in Precalculus

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