Question 1

Suppose the graph of $$f(x)$$ has a domain of $$[2, 8)$$ and a range of $$[-5, 7). $$What is the domain and range of the function $$g(x) = f(x-3) + 4$$?

Accepted Answer

Domain: $$[5, 11)$$, Range: $$[-1, 11)$$

Question 2

Given $$f(x) = x^2$, which of the following is the equation for the graph of f(x$$)$$ shifted 3 units to the right and 2 units down?

Accepted Answer

$$g(x) = (x-3)^2$ - 2$$

Question 3

If $$f(x) = |x|$$, what is the equation of the graph reflected about the $$y-$$axis and shifted up 4 units?

Accepted Answer

$$g(x) = |-x| + 4$$

Question 4

Which transformation will change the graph of $$y = f(x) to$$ $$y = -f(x+2)$$?

Accepted Answer

Reflect about the $$x-$$axis, then shift left 2 units

Question 5

If $$(2, 5) is a $$point on the graph of $$y = f(x)$$, what is the corresponding point on the graph of $$y = f(x-3) - 4$$?

Accepted Answer

$$(5, 1)$$

Question 6

Which of the following describes the transformation from $$y = f(x) to$$ $$y = f(-x)$$?

Accepted Answer

Reflection about the $$y-$$axis

Question 7

Given $$f(x) = \sqrt{x}$$, which function represents $$f(x)$$ shifted left 3 units, reflected about the $$y-$$axis, and then shifted down 2 units?

Accepted Answer

$$g(x) = -\sqrt{-x+3} - 2$$

Question 8

If the $$x-$$intercepts of $$y = f(x)$$ are $$-8$$ and $$1$$, what are the $$x-$$intercepts of $$y = f(x+3)$$?

Accepted Answer

$$-11$$ and $$-2$$

Question 9

Which function has a graph that is $$y = \sqrt{x}$$ shifted up 2 units then reflected about the $$x-$$axis?

Accepted Answer

$$h(x) = -\sqrt{x} - 2$$

Question 10

If $$(4, 7) is an $$absolute maximum point on the graph of $$f(x)$$, then which of the following is true for $$f(-x)$$?

Accepted Answer

$$(-4, 7) is an $$absolute maximum on $$f(-x)$$

Question 11

Which sequence of transformations will produce the graph of $$y = -f(-x+1) - 2$$ from $$y = f(x)$$?

Accepted Answer

Reflect about the $$y-$$axis, shift right 1 unit, reflect about the $$x-$$axis, shift down 2 units

Question 12

Given $$f(x) = x^3$, write the function that is shifted left 4 units, down 4 units, and reflected about the x$-axis.

Accepted Answer

$$g(x) = -(x+4)^3$ - 4$$

Question 13

If $$f(x) is $$increasing on $$(-1, 5)$$, for which interval is $$g(x) = f(x-2)$$ increasing?

Accepted Answer

$$(1, 7)$$

Question 14

Suppose $$f(x)$$ has an absolute minimum at $$x = 2. $$Where is the absolute minimum of $$g(x) = f(x+3)$$?

Accepted Answer

$$x = -1$$

Question 15

Which transformation will change the graph of $$y = f(x) to$$ $$y = f(x) - 5$$?

Accepted Answer

Shift the graph down 5 units

Question 16

If $$f(x)$$ has $$x-$$intercepts at $$x = -2$$ and $$x = 3$$, what are the $$x-$$intercepts of $$y = f(-x)$$?

Accepted Answer

$$x = 2$$ and $$x = -3$$

Question 17

Given $$f(x) = \sqrt{x}$$, which function is $$f(x)$$ reflected about the $$x-$$axis and then shifted down 3 units?

Accepted Answer

$$g(x) = -\sqrt{x} - 3$$

Question 18

If $$f(x) is $$decreasing on $$(2, 6)$$, on which interval is $$g(x) = f(-x)$$ decreasing?

Accepted Answer

$$(-6, -2)$$

Graphing Techniques and Transformations of Functions

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