Question 1

Which transformation is represented by the equation $$g(x) = f(x) + 3 if$$ $$f(x) = x^2$?

Accepted Answer

A vertical shift up by 3 units

Question 2

Given $$f(x) = x^2$, what is the effect of the transformation g(x$$) = $$(x-4)^2$$?

Accepted Answer

A horizontal shift right by 4 units

Question 3

If $$f(x) = x^2$, what is the equation for the graph reflected across the x-axis?

Accepted Answer

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

Question 4

Which transformation results in the equation $$g(x) = f(-x)$$?

Accepted Answer

Reflection across the y-axis

Question 5

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

Accepted Answer

Vertical stretch by a factor of 2

Question 6

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

Accepted Answer

Horizontal compression by a factor of 2

Question 7

Which of the following transformations does NOT change the x-intercepts of a function?

Accepted Answer

Vertical stretch/compression

Question 8

Suppose $$f(x) = x^2$. What is the equation after shifting f(x$$)$$ down by 3 units?

Accepted Answer

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

Question 9

Which transformation will result in the same graph as $$y = 4x^2$?

Accepted Answer

A vertical stretch of $$y = x^2$ by a factor of 4

Question 10

Which of the following is equivalent to $$y = (2x)^2$?

Accepted Answer

$$y = 4x^2$

Question 11

A parabola is shifted 3 units down. Which equation represents this transformation if the original is $$y = x^2$?

Accepted Answer

$$y = x^2$ - 3$$

Question 12

If $$f(x) = x^2$, which transformation will result in a graph that is narrower than the original?

Accepted Answer

$$g(x) = 4x^2$

Question 13

Which transformation does NOT alter the y-intercept of a function?

Accepted Answer

Horizontal stretch/compression

Question 14

If $$f(x) = x^2$, what is the result of reflecting f(x$$)$$ across the y-axis?

Accepted Answer

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

Question 15

Which transformation is described by $$g(x) = f(x+2)$$?

Accepted Answer

Horizontal shift left by 2 units

Question 16

A function $$f(x) is $$vertically compressed by a factor of 3. What is the new function?

Accepted Answer

$$g(x) = \frac{1}{3}f(x)$$

Question 17

Which transformation would change $$y = x^2$ to y$$ = $$(x+5)^2$$?

Accepted Answer

Shift left by 5 units

Question 18

Which of the following is a correct observation about the order of transformations?

Accepted Answer

The order of transformations can affect the resulting graph

Question 19

Which transformation would result in the same graph as a vertical stretch by 4 of $$y = x^2$?

Accepted Answer

A horizontal compression by a factor of 2

Question 20

If $$f(x) = x^2$, which transformation results in g(x) = f(-x$$)$$?

Accepted Answer

Reflection across the y-axis

Function Transformations: Shifts, Reflections, and Stretches

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