Question 1

Which of the following is the correct equation for a function whose graph has the shape of $$y = x^2$, but is upside-down, shifted right 6 units, and up 4 units?

Accepted Answer

$$y = -(x - 6)^2$ + 4$$

Question 2

Solve for $$x$$: $$x^2$$ - \frac{3}{3} = 2x$$

Accepted Answer

$$x = 1 or$$ $$x = 2$$

Question 3

Which of the following is the correct equation for a function with the shape of $$y = |x|$$, shifted left 8 units and up 7 units?

Accepted Answer

$$y = |x + 8| + 7$$

Question 4

Solve for $$x$$: $$\sqrt{x + 4} + 5 = 0$$

Accepted Answer

No real solution

Question 5

Given $$f(x) = x^4$ - 4x^2$ + 6$$, determine whether $$f(x) is $$even, odd, or neither.

Accepted Answer

Even

Question 6

Solve for $$x$$: $$\sqrt{x + 1} - 6 = 2$$

Accepted Answer

$$x = 49$$

Question 7

Find the zeros and their multiplicities for $$f(x) = (x + 2)^2$(x - 1).$$

Accepted Answer

Zero at $$x = -2 ($$multiplicity 2), $$x = 1 ($$multiplicity 1)

Question 8

Which of the following is the correct equation for a function with the shape of $$y = x^2$, upside-down, shifted left 5 units, and up 3 units?

Accepted Answer

$$y = -(x + 5)^2$ + 3$$

Question 9

Solve for $$x$$: $$x^3 - 4 = 4x$$ - $$x^2$$

Accepted Answer

$$x = 2 or$$ $$x = -2 or$$ $$x = 4$$

Question 10

Determine whether $$f(x) = 8x - 1 is $$one-to-one. If so, what is the formula for its inverse?

Accepted Answer

One-to-one, inverse is $$f^{-1}(x$$) = \frac{x + 1}{8}$$

Question 11

Solve for $$x$$: $$x - 3\sqrt{x} - 18 = 0$$

Accepted Answer

$$x = 9 or$$ $$x = 36$$

Question 12

Compute $$(-8 + 9i)^2$.

Accepted Answer

$$-127 - 144i$$

Question 13

Solve for $$x$$: $$7 - |4x + 3| = 2$$

Accepted Answer

$$x = 1.25 or$$ $$x = -2.5$$

Question 14

Solve for $$x$$: $$\sqrt{x + 4} + 2 = x$$

Accepted Answer

$$x = 4$$

Question 15

Which of the following is the correct solution to $$\frac{1}{x} + \frac{1}{x+1} = \frac{5}{6}$$?

Accepted Answer

$$x = 2 or$$ $$x = -3$$

Question 16

Solve for $$x$$: $$x^4$$ - $$12x^2 + 27 = 0$

Accepted Answer

$$x = \pm 3 or$$ $$x = \pm 1$$

Question 17

Which of the following is the correct solution to $$\frac{3x}{x+5} + \frac{15}{x} = \frac{75}{x^2$ + 5x}$$?

Accepted Answer

$$x = 3$$

Question 18

Given the function $$f(x) = (x + 2)^2$(x - 1)$$, which statement is true about the multiplicity of its zeros?

Accepted Answer

$$x = -2$$ has multiplicity 2, $$x = 1$$ has multiplicity 1

College Algebra: Function Transformations, Equations, and Properties – Study Guide

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