Question 1

Given the points $$P_1 = (-2$$, 4)$$ and P_2$ = (7, 0)$$, what is the exact distance $$d$$ between them?

Accepted Answer

$$d = \sqrt{(7 + 2)^2$ + (0 - 4)^2$} = \sqrt{81 + 16} = \sqrt{97}$$

Question 2

What is the midpoint of the line segment joining the points $$P_1 = (-2$$, 4)$$ and P_2$ = (7, 0)$$?

Accepted Answer

$$\left( \frac{5}{2}, 2 \right)$$

Question 3

What is the standard form of the equation of a circle with center $$(-6, 8)$$ and radius $$10$$?

Accepted Answer

$$(x + 6)^2$ + (y - 8)^2$ = 100$$

Question 4

A circle has the equation $$4(x - 4)^2$ + 4y^2$ = 36. $$What is its center and radius?

Accepted Answer

Center: $$(4, 0)$$, Radius: $$3$$

Question 5

Find the domain of the function $$f(x) = \frac{4}{3x - 27}.$$

Accepted Answer

$$(-\infty, 9) \cup (9, \infty)$$

Question 6

Given the quadratic function $$f(x) = x^2$ + 4x - 12$$, what is the vertex of the parabola?

Accepted Answer

$$(-2, -16)$$

Question 7

Suppose a manufacturer finds that revenue $$R(p)$$ for a gas dryer is $$R(p) = -6p^2$ + 24,000p. $$What unit price $$p$$ maximizes revenue?

Accepted Answer

$$p = 2,000$$

Question 8

Which of the following is the correct domain for the function $$g(x) = \sqrt{x - 2}$$?

Accepted Answer

$$[2, \infty)$$

Question 9

For the polynomial $$f(x) = (x - 6)^2$(x + 8)$$, what is the maximum number of turning points?

Accepted Answer

$$2$$

Question 10

Use the Remainder Theorem to find the remainder when $$f(x) = 3x^5$ - 3x - 17 is $$divided by $$x - 2.$$

Accepted Answer

$$f(2) = 3(32) - 3(2) - 17 = 96 - 6 - 17 = 73$$

Question 11

Which of the following is the correct inverse of the function $$f(x) = e$$^{x+4}$$?

Accepted Answer

$$f^{-1}(x$$) = \ln x - 4$$

Question 12

Solve the logarithmic equation $$\log x + \log(x - 3) = 1$$ for $$x.$$

Accepted Answer

$$x = 5$$

Question 13

Strontium-90 decays according to $$A(t) = 800e$$^{-0.024t}$$. How many grams remain after 10 years?

Accepted Answer

$$800e^{-0.24}$$ \approx 631$$ grams

Question 14

What is the domain of the function $$f(x) = \ln(x - 4)$$?

Accepted Answer

$$(4, \infty)$$

Question 15

Which of the following is the correct single logarithm for $$2\log 3u + 4\log 5v$$?

Accepted Answer

$$\log(9u^2$ \cdot 625v^4$)$$

Question 16

For the rational function $$R(x) = \frac{16x}{3x^2$}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 17

Which of the following functions is even?

Accepted Answer

$$g(x) = -3 - x^2$

Question 18

What is the solution set for the inequality $$(x - 1)(x - 2)(x - 9) \u003e 0$$?

Accepted Answer

$$(-\infty, 1) \cup (2, 9)$$

Question 19

Which of the following is the correct domain for the function $$f(x) = \frac{6x^4$}{x^2$}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Precalculus Study Guide: Analytic Geometry, Functions, and Polynomial Analysis

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