Question 1

Which of the following describes the transformation for $$y = f(x) + 4$$ compared to $$y = f(x)$$?

Accepted Answer

A vertical shift 4 units up

Question 2

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

Accepted Answer

Shift the graph 3 units to the right

Question 3

Which transformation results in a reflection of the graph of $$y = f(x)$$ over the y-axis?

Accepted Answer

$$y = f(-x)$$

Question 4

If $$f(x) = x^2$, which equation represents a vertical stretch by a factor of 3?

Accepted Answer

$$y = 3f(x)$$

Question 5

Given $$f(x) = x^2$, what is the result of the transformation y = f(x+2) - 5$?

Accepted Answer

Shift left 2 units and down 5 units

Question 6

Which of the following transformations will reflect the graph of $$y = f(x)$$ over the x-axis?

Accepted Answer

$$y = -f(x)$$

Question 7

Suppose $$f(x) = x^2$. What is the effect of the transformation y = f(2x$$)$$?

Accepted Answer

Horizontal shrink by a factor of 2

Question 8

Given $$f(x) = x^3$, which transformation results in y = -f(x) + 1$?

Accepted Answer

Reflect over the x-axis and shift up 1 unit

Question 9

If $$f(x) = \sqrt{x}$$, what is the effect of the transformation $$y = \sqrt{x-4} + 2$$?

Accepted Answer

Shift right 4 units and up 2 units

Question 10

Which transformation will result in a vertical shrink of the graph of $$y = f(x) by a $$factor of $$\frac{1}{2}$$?

Accepted Answer

$$y = \frac{1}{2}f(x)$$

Question 11

Given $$f(x) = x^2$, which transformation results in y = f(-x) + 3$?

Accepted Answer

Reflect over the y-axis and shift up 3 units

Question 12

A function $$f(x) is $$transformed to $$g(x) = 2f(x-1) - 3. $$Which sequence of transformations is correct?

Accepted Answer

Shift right 1 unit, vertical stretch by 2, shift down 3 units

Question 13

If $$f(x) = x^2$, what is the effect of the transformation y = f$$(\frac{1}{2}x)$$?

Accepted Answer

Horizontal stretch by a factor of 2

Question 14

Given $$f(x) = x^2$, which transformation results in y = -f(x-2) + 5$?

Accepted Answer

Shift right 2 units, reflect over x-axis, shift up 5 units

Question 15

Which of the following best describes the transformation $$y = f(-x) - 4$$?

Accepted Answer

Reflect over the y-axis and shift down 4 units

Question 16

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is modeled by $$h(t) = -5t^2$ + 20t + 2. If $$the entire path is shifted up by 3 meters, what is the new equation?

Accepted Answer

$$h(t) = -5t^2$ + 20t + 5$$

Question 17

Which transformation will result in a horizontal shift 5 units to the left for $$y = f(x)$$?

Accepted Answer

$$y = f(x+5)$$

Question 18

Given $$f(x) = x^2$, what is the effect of the transformation y = -2f(x+1$$)$$?

Accepted Answer

Reflect over x-axis, vertical stretch by 2, shift left 1 unit

Question 19

If $$f(x) = \sqrt{x}$$, which transformation results in $$y = -\sqrt{x-3} + 4$$?

Accepted Answer

Shift right 3 units, reflect over x-axis, shift up 4 units

Graphing Techniques and Transformations in College Algebra

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