Question 1

Which of the following equations represents the slope of the line passing through the points $$(8, 6)$$ and $$(5, 8)$$?

Accepted Answer

$$y = -\frac{2}{3}x + \frac{34}{3}$$

Question 2

Given the function $$f(x) = -5x^5$ - 7x^3$, determine whether the function is even, odd, or neither.

Accepted Answer

Odd

Question 3

A company offers an internet plan with the following piecewise cost function for $$x$$ hours of use per month:

$$C(x) = \begin{cases} 18 & 	ext{if } x \leq 50 \ 18 + 0.25(x-50) & 	ext{if } x \u003e 50 \end{cases}$$

What is the cost for 75 hours of use?

Accepted Answer

$$24.25$$

Question 4

Which of the following is the correct formula for the $$nth $$term of the arithmetic sequence $$4, 12, 20, 28, 36, \ldots$$?

Accepted Answer

$$a_n = 4 + 8(n-1)$$

Question 5

Given $$f(x) = x - 4$$ and $$g(x) = 4x - 8$$, what is $$(f \cdot g)(x)$$?

Accepted Answer

$$4x^2 - 24x + 32$

Question 6

Find the domain of the function $$g(x) = \frac{2x}{x-1}.$$

Accepted Answer

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

Question 7

Given the geometric sequence $$3, 9, 27, 81, 243, \ldots$$, what is the formula for the $$nth $$term?

Accepted Answer

$$a_n = 3(3$$)^{n-1}$$

Question 8

A basketball player signs a contract with a starting salary of $$830,000$$ per year and an annual increase of $$4.5\%$$ beginning in the second year. What will the athlete's salary be, to the nearest dollar, in the 7th year?

Accepted Answer

$$1,080,876$$

Question 9

Given $$f(x) = 8x + 14$$ and $$g(x) = 4x - 1$$, find $$(f \circ g)(2).$$

Accepted Answer

$$70$$

Question 10

Which of the following is the correct inverse of the function $$f(x) = \frac{8x + 5}{3}$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{3x - 5}{8}$$

Question 11

Given the function $$f(x) = \sqrt{2x - 4}$$, what is the domain?

Accepted Answer

$$[2, \infty)$$

Question 12

Given the arithmetic sequence $$-10, -6, -2, 2, 6, \ldots$$, what is the 20th term?

Accepted Answer

$$66$$

Question 13

Given $$f(x) = 4x^2$ + 2x + 6$$ and $$g(x) = 2x - 3$$, find $$(g \circ f)(1).$$

Accepted Answer

$$21$$

Question 14

Which of the following is the correct formula for the average rate of change of $$f(x) = \sqrt{2x}$$ from $$x_1 = 2$ to x_2$ = 8$$?

Accepted Answer

$$\frac{1}{3}$$

Question 15

Given the line $$y = -\frac{3}{5}x + 3$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$\frac{5}{3}$$

Question 16

Which of the following is the correct formula for the quadratic formula?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 17

Given the function $$f(x) = x^3$ + x^2$ - 4$$, determine whether the function is even, odd, or neither.

Accepted Answer

Neither

Question 18

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

Accepted Answer

$$2x^2$$ + $$x^4$$

Question 19

Given $$f(x) = x - 4$$ and $$g(x) = 4x - 8$$, what is $$\left(\frac{f}{g}\right)(x)$$?

Accepted Answer

$$\frac{x-4}{4x-8}$$

College Algebra Exam 1 Review – Step-by-Step Study Guidance

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