Question 1

Given the points $$A(2, -3)$$ and $$B(-4, 5)$$, what is the distance between $$A$$ and $$B$$?

Accepted Answer

$$10$$

Question 2

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

Accepted Answer

$$\{(0,1), (1,2), (2,3)\}$$

Question 3

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

Accepted Answer

$$19$$

Question 4

Which of the following equations is in point-slope form for a line passing through $$(3, -2)$$ with slope $$m = 4$$?

Accepted Answer

$$y + 2 = 4(x - 3)$$

Question 5

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

Accepted Answer

$$3$$

Question 6

Which of the following describes the graph of $$y = -|x - 3| + 2$$ compared to $$y = |x|$$?

Accepted Answer

Reflected over the $$x-$$axis, shifted right 3 units, up 2 units

Question 7

What is the vertex of the quadratic function $$f(x) = -2(x + 1)^2$ + 5$$?

Accepted Answer

$$(-1, 5)$$

Question 8

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 9

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -3x^2$ + 12x + 5$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$17 at$$ $$x = 2$$ thousand units

Question 10

Which of the following is the standard form of the equation of a line with slope $$-\frac{2}{3}$$ passing through $$(6, 1)$$?

Accepted Answer

Question 11

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

Accepted Answer

$$x \geq 1$$

Question 12

If $$f(x) = 3x - 4$$ and $$g(x) = x + 5$$, what is $$(f + g)(2)$$?

Accepted Answer

$$11$$

Question 13

Which of the following describes the graph of $$y = (x - 2)^3$ + 1$$ compared to $$y = x^3$?

Accepted Answer

Shifted right 2 units and up 1 unit

Question 14

Which of the following is the equation of a horizontal line passing through $$(4, -2)$$?

Accepted Answer

$$y = -2$$

Question 15

Given the piecewise function $$f(x) = \begin{cases} x + 2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$, what is $$f(-3) + f(2)$$?

Accepted Answer

$$7$$

Question 16

Which of the following is the correct midpoint of the segment joining $$(7, -1)$$ and $$(-3, 5)$$?

Accepted Answer

$$(2, 2)$$

Question 17

If $$f(x) = x^2$ - 4x + 3$$, for which value(s) of $$x is$$ $$f(x)$$ decreasing?

Accepted Answer

$$x \u003e 2$$

Question 18

Which of the following is the range of $$f(x) = |x| - 3$$?

Accepted Answer

$$y \geq -3$$

Question 19

A medical researcher models the temperature $$T (in$$ $$^ \circC) of a $$patient after medication as $$T(t) = -0.5t^2$ + 2t + 37$$, where $$t is $$hours after medication. What is the maximum temperature and when does it occur?

Accepted Answer

Maximum temperature is $$39 at$$ $$t = 2$$ hours

Question 20

Which of the following is the graph of $$y = \sqrt{x + 4}$$ obtained from $$y = \sqrt{x}$$?

Accepted Answer

Shifted left 4 units

College Algebra Study Guide: Graphs, Functions, and Linear & Quadratic Functions

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