Question 1

Given points $$P(-\sqrt{7}, 8\sqrt{3})$$ and $$Q(5\sqrt{7}, -\sqrt{13})$$, what is the distance between $$P$$ and $$Q$$?

Accepted Answer

$$\sqrt{(5\sqrt{7} + \sqrt{7})^2$ + (-\sqrt{13} - 8\sqrt{3})^2$}$$

Question 2

Which of the following equations represents a circle centered at $$(4, -2)$$ with radius $$5$$?

Accepted Answer

$$(x-4)^2$$ + $$(y+2)^2 = 25$

Question 3

Given the relation $$\{(-4, -2), (-1, 0), (3, 5)\}$$, what is the domain and range?

Accepted Answer

Domain: $$\{-4, -1, 3\}$$, Range: $$\{-2, 0, 5\}$$

Question 4

Which of the following graphs passes the vertical line test and is therefore a function?

Accepted Answer

A parabola opening upwards

Question 5

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

Accepted Answer

$$[1, \infty)$$

Question 6

Given $$f(x) = x^2$ + 3$$ and $$g(x) = -2x + 6$$, find $$(f+g)(5).$$

Accepted Answer

$$18$$

Question 7

Which of the following describes the transformation of $$f(x) to$$ $$f(x-4)$$?

Accepted Answer

Horizontal translation 4 units to the right

Question 8

If $$f(x) = |x|$$, which statement is true?

Accepted Answer

The function is even

Question 9

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{(x+h)^2$ - x^2$}{h}$$

Question 10

Given $$f(x) = 8x - 9$$ and $$g(x) = \sqrt{x-1}$$, what is the domain of $$(f+g)(x)$$?

Accepted Answer

$$[1, \infty)$$

Question 11

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

Accepted Answer

$$3x + y = 7$$

Question 12

Which function is continuous everywhere except at $$x=3$$?

Accepted Answer

$$f(x) = \frac{1}{x-3}$$

Question 13

If $$f(x) = x^3$ and g(x) = x+4$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(x+4)^3$$

Question 14

Which of the following is the equation of a line perpendicular to $$y = 2x + 1$$ and passing through $$(0, 3)$$?

Accepted Answer

$$y = -\frac{1}{2}x + 3$$

Question 15

Which of the following describes the graph of $$y = f(-x)$$ compared to $$y = f(x)$$?

Accepted Answer

Reflected across the y-axis

Question 16

Given $$f(x) = x^2$ - 4x + 2$$, what is $$f(-1)$$?

Accepted Answer

$$7$$

Question 17

Which of the following is the correct composition $$(g \circ f)(x) if$$ $$f(x) = \sqrt{x+4}$$ and $$g(x) = -\frac{2}{x}$$?

Accepted Answer

$$-\frac{2}{\sqrt{x+4}}$$

Question 18

Which of the following is the range of the squaring function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 19

Which of the following is true about the greatest integer function $$f(x) = \lfloor x \rfloor$$?

Accepted Answer

It is discontinuous at all integer values of $$x$$

College Algebra Study Guide: Coordinates, Functions, Graphs, and Operations

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