Question 1

Which of the following describes the effect of the transformation $$f(x) 	o f(x-3) + 2 on $$the graph of $$f(x)$$?

Accepted Answer

Shift the graph 3 units to the right and 2 units up.

Question 2

Given the function $$g(x) = -2|x+1|$$, which sequence of transformations is applied to the parent function $$f(x) = |x|$$?

Accepted Answer

Shift left 1, reflect over the x-axis, and vertically stretch by 2.

Question 3

What is the domain and range of the function $$f(x) = \sqrt{x-4}$$?

Accepted Answer

Domain: $$[4, \infty)$$, Range: $$[0, \infty)$$

Question 4

If $$f(x) = x^2$, what is the effect of the transformation h(x) = 3f(-x) - 5$?

Accepted Answer

Reflect over the y-axis, vertically stretch by 3, and shift down 5.

Question 5

Which of the following functions is an odd function?

Accepted Answer

$$f(x) = x^3$

Question 6

A medical researcher models the spread of a virus using $$f(x) = 2$$^{x-5}$$ + 10. $$What does the $$-5$$ inside the exponent represent?

Accepted Answer

A horizontal shift 5 units to the right.

Question 7

Which transformation will change the graph of $$f(x) = \sqrt{x} to$$ $$g(x) = -\sqrt{x+4} + 3$$?

Accepted Answer

Shift left 4, reflect over the x-axis, and shift up 3.

Question 8

Which of the following best describes the range of the absolute value function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 9

A company’s profit is modeled by $$P(x) = -2(x-3)^2$ + 5. $$What is the vertex of this parabola, and what does it represent in this context?

Accepted Answer

Vertex: $$(3, 5)$$; maximum profit of 5 occurs when $$x = 3.$$

Question 10

Which of the following is the correct sequence of transformations to obtain $$h(x) = 2\sqrt{-(x-1)} - 4$$ from $$f(x) = \sqrt{x}$$?

Accepted Answer

Shift right 1, reflect over the y-axis, vertically stretch by 2, shift down 4.

Question 11

Which of the following statements is true about the function $$f(x) = x^2$?

Accepted Answer

It is an even function because $$f(-x) = f(x).$$

Question 12

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

Accepted Answer

Reflect over the x-axis and shift left 2.

Question 13

Which of the following is the domain of the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

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

Question 14

A chemical reaction’s rate is modeled by $$R(t) = 5\sqrt{t-2}. $$What is the minimum value of $$t$$ for which the reaction rate is defined?

Accepted Answer

$$t = 2$$

Question 15

Which transformation will change the graph of $$f(x) = x^2$ to g(x$$) = $$(x+4)^2 - 7$?

Accepted Answer

Shift left 4 and down 7.

Question 16

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

Accepted Answer

It is neither even nor odd.

Question 17

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

Accepted Answer

Shift left 2 and down 3.

Question 18

Which of the following best describes the intervals where the function $$f(x) = |x| is $$increasing and decreasing?

Accepted Answer

Decreasing on $$(-\infty, 0)$$ and increasing on $$(0, \infty)$$

Transformations of Functions in College Algebra

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