Question 1

Solve the equation $$2x + 3 = 4x - 2$$ for $$x.$$

Accepted Answer

$$x = 2.5$$

Question 2

Which of the following is the solution to the inequality $$|7 - 2x| = 3$$?

Accepted Answer

$$x = 2 or$$ $$x = 5$$

Question 3

Find the midpoint of the segment with endpoints $$(10, 2)$$ and $$(-2, 6).$$

Accepted Answer

$$(4, 4)$$

Question 4

Find the equation of the line through $$(3, -2)$$ parallel to $$2x - y = 5.$$

Accepted Answer

$$y = 2x - 8$$

Question 5

Given $$f(x) = x^2$ + 2x - 3$$, what are the coordinates of the vertex?

Accepted Answer

$$(-1, -4)$$

Question 6

What is the end behavior of $$f(x) = 7x$$^{145}$$ - 9x^2$ + 2x - 1 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 7

Given $$f(x) = 2x + 3$$ and $$g(x) = 3x - 1$$, find $$(f \circ g)(x).$$

Accepted Answer

$$6x + 1$$

Question 8

Find the inverse of $$f(x) = 2x + 3.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 3}{2}$$

Question 9

Which of the following describes the transformation of $$y = -4|x - 2| + 3$$ from its parent function $$y = |x|$$?

Accepted Answer

Shift right 2, vertical stretch by 4, reflect over $$x-$$axis, shift up 3

Question 10

Given $$f(x) = \frac{3x}{(x+1)(x-2)}$$, which of the following are the vertical asymptotes?

Accepted Answer

$$x = -1$$ and $$x = 2$$

Question 11

Rewrite $$2 \log_m n - 3 \log_m z as a $$single logarithm with coefficient 1.

Accepted Answer

$$\log_m \left( \frac{n^2$}{z^3$} \right)$$

Question 12

Assuming all variables represent real numbers, use properties of logarithms to rewrite $$\log_b \frac{x}{y^2$}.$$

Accepted Answer

$$\log_b x - 2 \log_b y$$

Question 13

Solve for $$x$$: $$x = \log_3$ 81.$$

Accepted Answer

$$x = 4$$

Question 14

Given $$2^{x+1} = 32$, what is the value of x$?

Accepted Answer

$$x = 4$$

Question 15

Simplify $$\frac{4 + i}{7 - 3i}$$ and write in the form $$a + bi.$$

Accepted Answer

$$\frac{25}{58} + \frac{19}{58}i$$

Question 16

What is the discriminant of $$f(x) = x^2$ + 2x - 3$$ and what does it tell you about the zeros?

Accepted Answer

Discriminant is $$16$$, so there are two real zeros.

Question 17

Find the $$y-$$intercept of $$f(x) = \frac{3x}{(x+1)(x-2)}.$$

Accepted Answer

$$y = 0$$

Question 18

Which of the following is the correct horizontal asymptote for $$f(x) = \frac{3x}{(x+1)(x-2)}$$?

Accepted Answer

$$y = 0$$

Question 19

If $$f(x) = x^2$ + 2x - 3$$, what is the axis of symmetry?

Accepted Answer

$$x = -1$$

Precalculus Practice Final Study Guide: Key Concepts and Problem Types

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