Question 1

Given the points $$P_1 = (4$$, 7)$$ and P_2$ = (-2, -3)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(4 - (-2))^2$ + (7 - (-3))^2$} = \sqrt{36 + 100} = \sqrt{136}$$

Question 2

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$4 in $$standard form?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 16$$

Question 3

Find the $$x-$$intercepts of the equation $$25x^2$$ + $$4y^2 = 100$.

Accepted Answer

$$x = \pm 2$$

Question 4

Which of the following sets is NOT a function?

Accepted Answer

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

Question 5

Given the line $$y - 3 = 3(x - 4)$$, what is the equation of the line perpendicular to it that passes through $$(1, 8) in $$point-slope form?

Accepted Answer

$$y - 8 = -\frac{1}{3}(x - 1)$$

Question 6

What is the domain of the function $$f(x) = \sqrt{x - 3}$$?

Accepted Answer

$$x \geq 3$$

Question 7

For the function $$f(x) = 2x^2$ + x - 3$$, what is the average rate of change over the interval $$[0, 1]$$?

Accepted Answer

$$3$$

Question 8

Which of the following equations is symmetric with respect to the $$y-$$axis?

Accepted Answer

$$y = x^2$ - 9$$

Question 9

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

Accepted Answer

Question 10

What is the slope of the line given by $$3x + 4y = 12$$?

Accepted Answer

$$-\frac{3}{4}$$

Question 11

If a circle has the equation $$x^2$$ + $$y^2 + 6x + 4y - 12 = 0$, what is its center and radius?

Accepted Answer

Center $$(-3, -2)$$, radius $$5$$

Question 12

Which of the following best describes the symmetry of the equation $$x^2$$ + $$y^2 = 100$?

Accepted Answer

Symmetric to the $$x-$$axis, $$y-$$axis, and origin

Question 13

Given $$f(x) = 2x^2$ + 3x + 1$$ and $$g(x) = \frac{1}{x}$$, what is $$g(-1)$$?

Accepted Answer

$$-1$$

Question 14

A chemical reaction's temperature $$T (in$$ $$^\circC) is $$modeled by $$T(t) = 5t^2$ - 2t + 10$$, where $$t is $$time in minutes. What is the average rate of change of temperature from $$t = 2 to$$ $$t = 5$$?

Accepted Answer

$$35$$

Question 15

Which of the following best describes the domain of $$f(x) = \frac{5}{x^2$ - 2x + 3}$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 16

Given the function $$f(x) = 2x^2$ + x - 3$$, what is the equation of the secant line containing $$(0, f(0))$$ and $$(1, f(1))$$?

Accepted Answer

$$y = 3x - 3$$

Question 17

A medical researcher models the spread of a virus with $$y = x^2$ - 9. $$Which of the following statements about the graph is true?

Accepted Answer

It is symmetric to the $$y-$$axis

Question 18

Given the line $$y = 5x$$, what is the equation of the line perpendicular to it that passes through $$(-3, 4) in $$slope-intercept form?

Accepted Answer

$$y = -\frac{1}{5}x + \frac{17}{5}$$

Question 19

Which of the following best describes the intervals where the function $$f(x) = x^2$ - 9 is $$positive?

Accepted Answer

$$(-\infty, -3) \cup (3, \infty)$$

Precalculus Study Guide: Step-by-Step Guidance for Unit 1

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