Question 1

Which graph best represents the function $$f(x) = \sqrt{x+6}$$?

Accepted Answer

Graph 3

Question 2

Which transformation is represented by the function $$f(x) = \sqrt{x+7}$$ compared to its parent function $$f(x) = \sqrt{x}$$?

Accepted Answer

Shift to the left by 7

Question 3

True or False: All vertical transformations affect the x-coordinates of the basic (parent) function.

Accepted Answer

False

Question 4

Let $$f(x) = x^2$ + 11$$ and $$g(x) = x + 4. $$What is $$(f-g)(x)$$?

Accepted Answer

$$x^2 + 7$

Question 5

Let $$f(x) = x^2$ + 11$$ and $$g(x) = x + 4. $$What is $$(f+g)(3)$$?

Accepted Answer

$$24$$

Question 6

Let $$g(x) = x + 4. $$What is $$(g \cdot g)(x)$$?

Accepted Answer

$$x^2 + 8x + 16$

Question 7

Let $$f(x) = x^2$ + 11$$ and $$g(x) = x + 4. $$What is $$(g \circ f)(x)$$?

Accepted Answer

$$(x^2 + 11) + 4$

Question 8

Let $$f(x) = \sqrt{1-x}$$ and $$h(x) = 4x^3$. What is (f-h)(-3$$)$$?

Accepted Answer

$$\sqrt{1-(-3)} - 4(-3)^3$

Question 9

Let $$f(x) = \sqrt{1-x}$$ and $$h(x) = 4x^3$. What is (f$$ \cdot h)(3)$$?

Accepted Answer

$$\sqrt{1-3} \cdot 4 \cdot 3^3$

Question 10

Let $$h(x) = 4x^3$. What is (h$$ \circ h)(x)$$?

Accepted Answer

$$4(4x^3)^3$

Question 11

Determine whether $$g(x) = 4x^3$ - x is $$odd, even, or neither.

Accepted Answer

Odd

Question 12

Determine whether $$f(x) = 2x^2$ - 5 is $$odd, even, or neither.

Accepted Answer

Even

Question 13

Determine whether $$h(x) = 2x^2$ - 3x + 7 is $$odd, even, or neither.

Accepted Answer

Neither

Question 14

Which graph best represents the function $$f(x) = |x|$$?

Accepted Answer

None of the above

Question 15

Which graph best represents the function $$f(x) = |x-5|$$?

Accepted Answer

None of the above

Question 16

Which graph best represents the function $$f(x) = -3x^3$?

Accepted Answer

None of the above

Question 17

A company’s profit $$P(x) in $$thousands of dollars is modeled by $$P(x) = x^2$ + 11$$, where $$x is $$the number of units sold in hundreds. If the company sells 5 hundred units, what is the profit?

Accepted Answer

$$P(5) = 25 + 11 = 36$$ thousand dollars

Study Guide for Algebra: Functions, Transformations, and Operations

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