Question 1

Which of the following sets contains only irrational numbers?

Accepted Answer

$$\{ \sqrt{5}, \pi, -\sqrt{2} \}$$

Question 2

What is the solution set to the inequality $$|3x + 2| \u003c 5$$?

Accepted Answer

$$(-\frac{7}{3}, 1)$$

Question 3

A population grows according to $$P(t) = 120e$$^{0.015t}$$. What is the doubling time for this population?

Accepted Answer

$$\frac{\ln 2}{0.015}$$

Question 4

Given $$f(x) = \sqrt{x + 4}$$, what is the domain of $$f in $$interval notation?

Accepted Answer

$$[-4, \infty)$$

Question 5

Which transformation describes $$g(x) = -2f(x + 3) - 5$$ relative to $$f(x)$$?

Accepted Answer

Shift left 3, reflect over x-axis, vertical stretch by 2, shift down 5

Question 6

Solve the equation $$5 + \sqrt{x + 7} = x. $$Which value(s) are valid solutions?

Accepted Answer

$$x = 9$$

Question 7

If $$f(x) = x^2$ + 2x - 3$$, what is the difference quotient $$\frac{f(x + h) - f(x)}{h}$$ simplified?

Accepted Answer

$$2x + h + 2$$

Question 8

Which of the following is the correct vertex for the quadratic $$f(x) = -x^2$ + 14x - 47$$?

Accepted Answer

$$(7, 2)$$

Question 9

What is the horizontal asymptote of $$f(x) = \frac{6x^4$ - 3x^2$ + 1}{9x^4$ + 3x - 2}$$?

Accepted Answer

$$y = \frac{2}{3}$$

Question 10

Given $$f(x) = 2x^3$ - 3x^2$ - 11x + 6$$, which of the following is NOT a possible rational zero according to the Rational Zeros Theorem?

Accepted Answer

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

Question 11

A circle has equation $$(x + 3)^2$ + (y - 2)^2$ = 16. $$What is its center and radius?

Accepted Answer

Center $$(-3, 2)$$, radius $$4$$

Question 12

Which of the following is the correct result for $$(8xy^5)(-8x$$^{-8}$$y)$?

Accepted Answer

$$-64\frac{y^6$}{x^7$}$$

Question 13

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

Accepted Answer

$$3x^2 + 3x - 10$

Question 14

Which of the following is the correct expanded form of $$\log_a(x^2$y^5/z^4$)$$?

Accepted Answer

$$2\log_a x + 5\log_a y - 4\log_a z$$

Question 15

What is the solution to $$2^{3x - 7} = 32$?

Accepted Answer

$$x = 4$$

Question 16

Which of the following is the correct domain for $$h(x) = \frac{3x^2$ - x + 7}{x^2$ + 2x - 3}$$?

Accepted Answer

$$x 
eq -3, 1$$

Question 17

If $$y$$ varies inversely with $$x$$ and $$y = 22$$ when $$x = 0.4$$, what is the equation relating $$x$$ and $$y$$?

Accepted Answer

$$y = \frac{8.8}{x}$$

Question 18

What is the result of $$\sqrt{245x^6$y^5$$}$ simplified?

Accepted Answer

$$7y^2$$|$$x^3$$|\sqrt{5y}$$

College Algebra Comprehensive Study Guide: Key Concepts and Formulas

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