Question 1

Which of the following is the correct domain and range for the square root function $$f(x) = \sqrt{x}$$?

Accepted Answer

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

Question 2

If $$f(x) = x^2$, which transformation results in the graph of g(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units, then up 2 units

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = |x|$$

Question 4

What is the effect of the transformation $$y = -f(x) on $$the graph of $$y = f(x)$$?

Accepted Answer

Reflection about the x-axis

Question 5

Given $$f(x) = x^3$, what is the domain and range of f(x$$)$$?

Accepted Answer

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

Question 6

Which transformation will produce the graph of $$y = 2f(x)$$ from $$y = f(x)$$?

Accepted Answer

Vertical stretch by a factor of 2

Question 7

If $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = |x+4|$$?

Accepted Answer

Shift the graph 4 units to the left

Question 8

Which of the following describes the transformation from $$f(x) to$$ $$f(2x)$$?

Accepted Answer

Horizontal shrink by a factor of 2

Question 9

A real-world scenario: The height $$h (in $$meters) of a diver above water is modeled by $$h(t) = -5(t-2)^2$ + 10. $$Which transformation has been applied to the standard quadratic function $$f(t) = -5t^2$?

Accepted Answer

Shift right 2 units and up 10 units

Question 10

Which of the following is the correct sequence of transformations to obtain $$y = 3\sqrt{x-1} + 2$$ from $$y = \sqrt{x}$$?

Accepted Answer

Shift right 1 unit, vertically stretch by 3, shift up 2 units

Question 11

Which function is odd?

Accepted Answer

$$f(x) = x^3$

Question 12

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

Accepted Answer

Reflect about the x-axis and shift left 2 units

Question 13

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

Accepted Answer

Shift the graph down 5 units

Question 14

Given $$f(x) = x^2$, which transformation results in g(x$$) = \frac{1}{2}f(x)$$?

Accepted Answer

Vertical shrink by a factor of $$\frac{1}{2}$$

Question 15

Which of the following is the correct transformation for $$y = f(-x)$$?

Accepted Answer

Reflection about the y-axis

Question 16

A medical imaging device uses the function $$f(x) = \sqrt{x} to $$model signal intensity. If the input is delayed by 3 units and the output is doubled, which function models the new signal?

Accepted Answer

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

Question 17

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

Accepted Answer

Shift left 1 unit, vertically shrink by $$\frac{1}{2}$$, reflect about the x-axis, shift up 4 units

Question 18

Which of the following describes the transformation from $$f(x) to$$ $$f\left(\frac{x}{3}\right)$$?

Accepted Answer

Horizontal stretch by a factor of 3

Question 19

A population of bacteria is modeled by $$P(t) = 1000 + 200|t-5|. $$What transformation has been applied to the absolute value function?

Accepted Answer

Shift right 5 units, vertically stretch by 200, shift up 1000 units

Transformations of Functions: Precalculus Study Notes

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