Question 1

Which of the following transformations results in a horizontal compression of the graph of $$y = x^2$?

Accepted Answer

$$y = (2x)^2$

Question 2

Given the function $$f(x) = x^2$, which transformation produces a vertical stretch by a factor of 2?

Accepted Answer

$$f(x) = 2x^2$

Question 3

If you square both sides of an equation, what must you always do before finalizing your solution?

Accepted Answer

Check for extraneous solutions by substituting back into the original equation.

Question 4

What is the domain of the function $$f(x) = \sqrt{2x-8}$$?

Accepted Answer

$$x \geq 4$$

Question 5

Which of the following best describes the transformation from $$y = x^2$ to y$$ = \left(\frac{1}{2}x\$$right)^2$$?

Accepted Answer

Horizontal stretch

Question 6

Given $$f(x) = x^2$, what is the effect of the transformation f(-x$$)$$?

Accepted Answer

Reflection across the y-axis

Question 7

Which of the following equations could have extraneous solutions introduced during the solving process?

Accepted Answer

$$\sqrt{x+3} = x-1$$

Question 8

If $$f(x) = x^2$, what is the average rate of change from x = 1$ to x = 3$?

Accepted Answer

$$4$$

Question 9

Which of the following is NOT a function?

Accepted Answer

$$x = y^2$

Question 10

What is the slope of the line passing through the points $$(2, 5)$$ and $$(6, 13)$$?

Accepted Answer

$$2$$

Question 11

Which transformation results in a vertical compression of the graph of $$y = x^2$?

Accepted Answer

$$y = \frac{1}{2}x^2$

Question 12

If $$f(x) = x^2$, what is the result of the transformation f(x-3$$)$$?

Accepted Answer

Shift right by 3 units

Question 13

Which of the following is the correct formula for the difference quotient of $$f(x)$$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h}$$

Question 14

Which of the following describes the transformation $$y = -x^2$?

Accepted Answer

Reflection across the x-axis

Question 15

What is the domain of the function $$f(x) = \frac{1}{x-5}$$?

Accepted Answer

$$x 
eq 5$$

Question 16

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of g(f(x$$))$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 17

Which of the following is the correct process for finding the inverse of a function $$y = f(x)$$?

Accepted Answer

Switch $$x$$ and $$y$$, then solve for $$y$$

Question 18

Which of the following is a necessary condition for a function to have an inverse that is also a function?

Accepted Answer

It passes the horizontal line test.

Question 19

If $$f(x) = x^2$ and g(x$$) = $$2x^2$$, which graph is a vertical stretch of the other?

Accepted Answer

$$g(x) is a $$vertical stretch of $$f(x)$$

Question 20

Which of the following is true about the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

The domain is $$x \geq 2$$

Key Concepts in Equations, Functions, and Transformations (College Algebra Study Notes)

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