$$(f \circ g)(x) = (\sqrt{x-8})^2$ = x-8$$, \text{ domain: } [8, \infty)$

Question 1

Which of the following represents a vertical reflection of the function $$f(x)$$?

Accepted Answer

$$-f(x)$$

Question 2

Given $$f(x) = x^2$, what is the equation for the function g(x$$)$$ that is f(x$$)$$ shifted 3 units to the right and 2 units up?

Accepted Answer

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

Question 3

If $$f(x) = |x|$$, which transformation results in $$g(x) = -4|x|$$?

Accepted Answer

Reflection over the $$x-$$axis and vertical stretch by 4

Question 4

Given $$f(x) = \sqrt{x-2}$$, what is the equation for $$g(x) if$$ $$g(x) is a $$reflection of $$f(x)$$ about the $$y-$$axis?

Accepted Answer

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

Question 5

Which transformation will move the graph of $$f(x)$$ down by 5 units?

Accepted Answer

$$f(x) - 5$$

Question 6

If $$f(x) = x^3$, write the equation for h(x$$)$$ if f(x$$)$$ is reflected over the x$-axis and then shifted down 2 units.

Accepted Answer

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

Question 7

Which of the following describes a horizontal shrink by a factor of 2 for the function $$f(x)$$?

Accepted Answer

$$f(2x)$$

Question 8

Given $$f(x) = x^2$ and g(x$$) = $$x^2 + x + 2$, what is the domain of f(x) + g(x$$)$$?

Accepted Answer

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

Question 9

If $$f(x) = \sqrt{x}$$ and $$g(x) = 3x - 6$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$[0, 2) \cup (2, \infty)$$

Question 10

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x-8}$$, find (f$$ \circ g)(x)$$ and its domain.

Accepted Answer

$$(f \circ g)(x) = (\sqrt{x-8})^2$ = x-8$$, 	ext{ domain: } [8, \infty)$

Question 11

Which of the following is the correct composition for $$h(x) = \frac{1}{x^2$ + 3x - 10} as$$ $$h(x) = (f \circ g)(x)$$?

Accepted Answer

$$f(x) = \frac{1}{x}, \quad g(x) = x^2$ + 3x - 10$$

Question 12

If $$f(x) = x^2$ and g(x) = x - 1$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$(f \circ g)(3) = f(g(3)) = f(2) = 4$$

Question 13

Which transformation(s) would result in the function $$f(x)$$ being reflected over the $$y-$$axis and shifted 2 units up?

Accepted Answer

$$f(-x) + 2$$

Question 14

Given $$f(x) = x^2$ with domain $$(-\infty, \infty)$$ and range $$[0, \infty)$$, what is the domain and range of g(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[2, \infty)$$

Question 15

If $$f(x) = x^2$ and g(x$$) = $$x^2 + x + 2$, what is (f + g)(x$$)$$?

Accepted Answer

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

Question 16

Given $$h(x) = 2x^3$ - 4$$ and $$k(x) = x^2$ + 2$$, what is $$(h \cdot k)(x)$$?

Accepted Answer

$$(h \cdot k)(x) = 2x^5$ + 4x^3$ - 4x^2$ - 8$$

College Algebra: Transformations and Operations with Functions

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