Question 1

Which transformation is applied to the parent function $$y = f(x) to $$obtain $$y = f(x) + 3$$?

Accepted Answer

A vertical shift 3 units up

Question 2

Given the function $$y = -2f(x - 4) + 1$$, which sequence of transformations is correct?

Accepted Answer

Shift right 4 units, reflect over x-axis, vertically stretch by 2, shift up 1 unit

Question 3

If $$f(x) = x^2$, what is the equation for the graph that is shifted 2 units left and 5 units down?

Accepted Answer

$$y = (x + 2)^2$ - 5$$

Question 4

Which of the following represents a vertical stretch of $$f(x) by a $$factor of 3 and a reflection over the x-axis?

Accepted Answer

$$y = -3f(x)$$

Question 5

Given the graph of $$y = f(x) as $$shown in image 2, what is the effect of the transformation $$y = f(x) - 2$$?

Accepted Answer

The entire graph shifts down by 2 units

Question 6

If $$g(x) = f(-x)$$, what transformation has been applied to $$f(x)$$?

Accepted Answer

Reflection over the y-axis

Question 7

Suppose $$f(x) = x^2$. What is the domain and range of g(x) = (x$$ - $$1)^2 + 3$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[3, \infty)$$

Question 8

Which equation represents the graph in image 3?

Accepted Answer

$$y = (x - 1)^2$ + 3$$

Question 9

A company models its profit with $$P(x) = 2f(x + 1) - 5$$, where $$f(x) is $$the base profit function. What does the $$+1$$ inside the function represent?

Accepted Answer

A horizontal shift 1 unit left

Question 10

Given $$y = f(x) as in $$image 2, what is the new vertex of the parabola if the function is transformed to $$y = f(x - 3) + 2$$?

Accepted Answer

The vertex shifts 3 units right and 2 units up

Question 11

If $$f(x) is $$reflected over the x-axis and then shifted down by 4 units, what is the equation?

Accepted Answer

$$y = -f(x) - 4$$

Question 12

Which transformation will change $$y = f(x) to$$ $$y = f(2x)$$?

Accepted Answer

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

Question 13

A medical researcher models the spread of a virus with $$V(x) = 0.5f(x - 7) + 100$$, where $$f(x) is $$the base infection curve. What does the $$+100$$ represent?

Accepted Answer

A vertical shift 100 units up

Question 14

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

Accepted Answer

Reflect over x-axis and shift left 2 units

Question 15

Which transformation sequence is used to obtain $$y = 3f(-x) + 2$$ from $$y = f(x)$$?

Accepted Answer

Reflect over y-axis, vertically stretch by 3, shift up 2 units

Question 16

A real-world scenario: The height $$h (in $$meters) of a projectile is modeled by $$h(t) = -5(t - 2)^2$ + 10. $$What does the $$(t - 2)$$ represent?

Accepted Answer

The maximum height occurs at $$t = 2$$ seconds

Transformations of Functions: Precalculus Study Notes

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