Question 1

Which transformation is represented by the function $$y = f(x) + 4$$?

Accepted Answer

A vertical translation 4 units up

Question 2

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

Accepted Answer

It shifts the graph 3 units to the right

Question 3

If $$h(x) = -f(x)$$, how does the graph of $$h(x)$$ relate to the graph of $$f(x)$$?

Accepted Answer

It is reflected across the x-axis

Question 4

Suppose $$f(x) = x^3$ - 4x^2$. What is the result of the transformation g(x) = f(-x$$)$$?

Accepted Answer

The graph is reflected across the y-axis

Question 5

Which transformation is described by $$y = f(x) - 7$$?

Accepted Answer

A vertical translation 7 units down

Question 6

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

Accepted Answer

The graph is stretched vertically by a factor of 2

Question 7

If $$y = f(-x)$$, which of the following is true?

Accepted Answer

The graph is reflected across the y-axis

Question 8

A medical researcher models the spread of a virus with $$f(x)$$, where $$x is $$days since outbreak. If the model is updated to $$g(x) = f(x+5)$$, what does this transformation represent?

Accepted Answer

The outbreak is modeled as starting 5 days earlier

Question 9

Given $$f(x) = |x|$$, what is the effect of the transformation $$y = f(2x)$$?

Accepted Answer

The graph is shrunk horizontally by a factor of 2

Question 10

A chemical reaction rate is modeled by $$f(x). If $$the rate is doubled, which transformation best represents this change?

Accepted Answer

$$y = 2f(x)$$

Question 11

Which transformation will move the graph of $$y = f(x) 6 $$units to the left?

Accepted Answer

$$y = f(x+6)$$

Question 12

If $$y = 0.5f(x)$$, what happens to the graph of $$y = f(x)$$?

Accepted Answer

It is shrunk vertically by a factor of 0.5

Question 13

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

Accepted Answer

The graph is reflected across the y-axis

Question 14

A city’s population growth is modeled by $$f(x). If $$the model is updated to $$y = f(x) - 1000$$, what does this transformation represent?

Accepted Answer

The population is decreased by 1000

Question 15

Which transformation will reflect the graph of $$y = f(x)$$ across the y-axis and then shift it 2 units up?

Accepted Answer

$$y = f(-x) + 2$$

Question 16

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

Accepted Answer

Shift the graph 3 units left and 2 units down

Question 17

If $$y = -2f(x)$$, what is the combined effect on the graph of $$y = f(x)$$?

Accepted Answer

It is reflected across the x-axis and stretched vertically by a factor of 2

Question 18

A company’s profit is modeled by $$f(x). If $$the model is updated to $$y = f(0.5x)$$, what does this transformation represent?

Accepted Answer

The graph is stretched horizontally by a factor of 2

Question 19

Given $$f(x) = x^3$ - 4x^2$, what is the result of the transformation h(x) = -f(x$$)$$?

Accepted Answer

The graph is reflected across the x-axis

Transformations of Functions (Section 2.5) – Precalculus Study Notes

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