Question 1

Which of the following describes the effect of multiplying a function $$f(x) by a $$constant $$a \u003e 1 to $$obtain $$g(x) = a f(x)$$?

Accepted Answer

The graph of $$g(x) is a $$vertical stretching of $$f(x).$$

Question 2

Given $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = 2|x| on $$the graph of $$f(x)$$?

Accepted Answer

The graph of $$g(x) is $$narrower than $$f(x).$$

Question 3

Suppose $$f(x) is a $$function. Which transformation results in a reflection of $$f(x)$$ across the x-axis?

Accepted Answer

$$g(x) = -f(x)$$

Question 4

A function $$f(x) is $$reflected across the y-axis. Which of the following equations represents this transformation?

Accepted Answer

$$g(x) = f(-x)$$

Question 5

Which of the following is true about the symmetry of the graph of $$y = x^2$ + 4$$?

Accepted Answer

It is symmetric with respect to the y-axis.

Question 6

If $$f(x) is an $$even function, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = f(x)$$

Question 7

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 8

A function $$f(x) is $$translated 4 units up and 2 units to the right. Which equation represents this transformation?

Accepted Answer

$$g(x) = f(x - 2) + 4$$

Question 9

Which of the following statements about symmetry is correct?

Accepted Answer

A graph symmetric with respect to both axes is also symmetric with respect to the origin.

Question 10

Given $$f(x) = \sqrt{x}$$, what is the effect of the transformation $$g(x) = -\sqrt{x}$$?

Accepted Answer

The graph of $$g(x) is $$reflected across the x-axis.

Question 11

Which transformation results in a horizontal shrinking of the graph of $$f(x)$$?

Accepted Answer

$$g(x) = f(ax)$$, \ a \u003e 1$

Question 12

A real-world scenario: The cost $$C (in $$dollars) to produce $$x$$ units of a product is modeled by $$C(x) = 5x + 100. If $$the cost function is shifted 20 units down due to a subsidy, what is the new cost function?

Accepted Answer

$$C(x) = 5x + 80$$

Question 13

Which of the following is NOT a property of even functions?

Accepted Answer

Their graphs are symmetric with respect to the origin.

Question 14

If $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = |x + 3|$$?

Accepted Answer

The graph of $$g(x) is $$translated 3 units to the left.

Question 15

Which of the following is true about the graph of $$x^2$$ + $$y^2 = 16$?

Accepted Answer

It is symmetric with respect to the x-axis, y-axis, and the origin.

Question 16

A function $$f(x) is $$translated $$k$$ units up. Which equation represents this transformation?

Accepted Answer

$$g(x) = f(x) + k$$

Question 17

Which of the following is a necessary condition for a function to be odd?

Accepted Answer

$$f(-x) = -f(x)$$ for all $$x in $$the domain.

Question 18

Given $$f(x) = x^2$, what is the effect of the transformation g(x) = -f(x - 2) + 3$?

Accepted Answer

The graph is reflected across the x-axis, shifted 2 units right, and 3 units up.

Question 19

Which of the following statements is true about the symmetry of the graph $$y = x^3$?

Accepted Answer

It is symmetric with respect to the origin.

Graphing Techniques: Stretching, Shrinking, Reflecting, Symmetry, and Translations

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