Q: If $$f(x) = 2x - 5$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

$$f(g(2)) = 2 \times 4 - 5 = 3$$

Question 1

Which of the following equations represents a circle in standard form with center at $$(-1, 4)$$ and radius $$5$$?

Accepted Answer

$$(x + 1)^2$ + (y - 4)^2$ = 25$$

Question 2

Given the points $$(2, -3)$$ and $$(6, 5)$$, what is the distance between them?

Accepted Answer

$$
\sqrt{(6-2)^2$ + (5-(-3))^2$} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5}
$$

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 4

A line passes through the points $$(1, 2)$$ and $$(4, 8). $$What is its slope?

Accepted Answer

$$
\frac{8-2}{4-1} = \frac{6}{3} = 2
$$

Question 5

Which of the following lines is perpendicular to the line $$y = -\frac{1}{2}x + 3$$?

Accepted Answer

$$y = 2x - 1$$

Question 6

A phone company charges a flat fee of $$5 plus 0.05 $$per minute. If your monthly bill is $45.20, how many minutes did you use?

Accepted Answer

$$
\frac{45.20 - 5}{0.05} = 804
$$

Question 7

Which of the following is the equation of a line parallel to $$y = 3x - 4$$ and passing through $$(2, 5)$$?

Accepted Answer

$$y = 3x - 1$$

Question 8

What is the midpoint of the segment joining $$(7, -2)$$ and $$(-3, 4)$$?

Accepted Answer

$$(2, 1)$$

Question 9

Which of the following statements is true about the graph of $$y = |x|$$?

Accepted Answer

It is symmetric about the y-axis.

Question 10

Given the equation $$x^2 + 2x$$ + $$y^2 - 8y + 8 = 0$, what is the center and radius of the circle?

Accepted Answer

Center $$(-1, 4)$$, radius $$3$$

Question 11

If $$f(x) = 2x - 5$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 2 	imes 4 - 5 = 3$$

Question 12

Which of the following is the slope-intercept form of the equation of a line passing through $$(-4, 3)$$ and perpendicular to $$y = \frac{1}{2}x - 6$$?

Accepted Answer

$$y = -2x - 5$$

Question 13

Which of the following is the correct definition of an x-intercept?

Accepted Answer

The point where the graph crosses the x-axis, with y-value always zero.

Question 14

If $$f(x) = x^2$ - 4x + 3$$, what are the x-intercepts?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 15

Which of the following is the equation of a vertical line passing through $$(3, -2)$$?

Accepted Answer

$$x = 3$$

Question 16

If two lines have slopes $$m_1$$ and $$m_2$$ such that $$m_1$$ $$m_2 = -1$, what can be said about the lines?

Accepted Answer

They are perpendicular.

Question 17

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 18

A function $$f is $$one-to-one if:

Accepted Answer

Each $$x in $$the domain corresponds to exactly one $$y in $$the range, and each $$y in $$the range corresponds to exactly one $$x in $$the domain.

Question 19

If $$f(x) = 3x + 2$$ and $$g(x) = x - 1$$, what is $$(g \circ f)(2)$$?

Accepted Answer

$$g(f(2)) = g(8) = 8 - 1 = 7$$

Precalculus Study Guide: The Rectangular Coordinate System, Graphs, and Linear Equations

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