Question 1

Which of the following is the correct equation for a function with 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

A function has the shape of $$y = |x|$$, but is shifted left 8 units and up 7 units. Which equation represents this transformation?

Accepted Answer

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

Question 3

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

Accepted Answer

$$x = 2, x = -1$$

Question 4

Which of the following is the correct solution to $$\sqrt{x+4} + 5 = 0$$?

Accepted Answer

No real solution

Question 5

Solve for $$x$$: $$\sqrt{4x+1} - 6 = 2$$

Accepted Answer

$$x = 13$$

Question 6

Which of the following is the correct solution to $$x^3 - 4 = 4x$$ - $$x^2$$?

Accepted Answer

$$x = 4, x = -2, x = 2$$

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

$$x = 9, x = 36$$

Question 9

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

Accepted Answer

Even

Question 10

Find the zeros of the function $$f(x) = (x+2)^2$(x-1)$$ and state the multiplicity of each zero.

Accepted Answer

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

Question 11

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

Accepted Answer

$$x = 1, x = -\frac{5}{2}$$

Question 12

Which of the following best describes the transformation for $$y = -(x+5)^2$ + 3$$?

Accepted Answer

Upside-down parabola, shifted left 5 units, up 3 units

Question 13

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

Accepted Answer

$$x = 4$$

Question 14

Which of the following is the correct solution to $$x^4$$ - $$12x^2 + 27 = 0$?

Accepted Answer

$$x = 3, x = -3, x = \sqrt{3}, x = -\sqrt{3}$$

Question 15

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

Accepted Answer

The graph touches the x-axis at $$x = -2$$ and crosses at $$x = 1$$

Question 16

Solve for $$x$$: $$\frac{3x}{x+5} + \frac{15}{x} = \frac{75}{x^2$+5x}$$

Accepted Answer

$$x = 5$$

Question 17

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

Accepted Answer

$$x = 2, x = -3$$

Question 18

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

Accepted Answer

$$-127 - 144i$$

Question 19

Which of the following best describes a function that is constant on an interval?

Accepted Answer

The function's output does not change as the input changes within that interval.

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

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