APPCU1T6

The graph of 𝑦 = 𝑓(𝑥), consisting of three line segments, is shown for −2 ≤ 𝑥 ≤ 4. The graph of 𝑦 = 𝑔(𝑥) is the result of transforming the graph of 𝑓. Which of the following gives the transformation from 𝑓 to 𝑔?

• 𝑔(𝑥) = 𝑓(𝑥 − 2) − 3

• 𝑔(𝑥) = 𝑓(𝑥 − 2) + 3

• 𝑔(𝑥) = 𝑓(𝑥 + 2) − 3

• 𝑔(𝑥) = 𝑓(𝑥 + 2) + 3

The graph of 𝑦 = 𝑓(𝑥), consisting of three line segments, is shown for −2 ≤ 𝑥 ≤ 4. The graph of 𝑦 = ℎ(𝑥) is the result of transforming the graph of 𝑓. Which of the following gives the transformation from 𝑓 to ℎ?

The graph of 𝑦 = 𝑘(𝑥), consisting of three line segments, is shown for −2 ≤ 𝑥 ≤ 4. The graph of 𝑦 = 𝑚(𝑥) is the result of transforming the graph of 𝑘. Which of the following gives the transformation from 𝑘 to 𝑚?

Let 𝑘 be a function that is a transformation of the function ℎ such that 𝑘(𝑥) = 3ℎ(𝑥 − 2). Which of the following lists the transformations that can be applied to the graph of ℎ that results in the graph of 𝑘?

• A vertical dilation by a factor of 3, followed by a horizontal translation by −2.

• A vertical dilation by a factor of 3, followed by a horizontal translation by 2.

Let 𝑝 be a function that is a transformation of the function 𝑚 such that 𝑝(𝑥) = −𝑚(𝑥 + 2) + 1. Which of the following lists the transformations that can be applied to the graph of 𝑚 that results in the graph of 𝑝?

• A reflection over the 𝑥-axis, a horizontal translation by −2, and a vertical translation by 1.

• A reflection over the 𝑥-axis, a horizontal translation by 2, and a vertical translation by −1.

• A reflection over the 𝑦-axis, a horizontal translation by −2, and a vertical translation by 1.

• A reflection over the 𝑦-axis, a horizontal translation by 2, and a vertical translation by −1.

The function ℎ is constructed by applying three transformations to the graph of 𝑓 in this order: a horizontal dilation by a factor of 2, a vertical dilation by a factor of 3, and a vertical translation by 1 unit. Which of the following gives the expression for ℎ in terms of 𝑓?

• 1 3 3 1

• 1 4 6 4 1

• 1 5 10 10 5 1

• 1 2 3 4 3 2 1

The function 𝑓(𝑥) has domain −6 ≤ 𝑥 ≤ 10 and range 0 ≤ 𝑦 ≤ 4. The graph of 𝑔(𝑥) is the result of the transformation 𝑔(𝑥) = 𝑓(𝑥 + 2) − 3. Which of the following gives the domain of 𝑔(𝑥)?

• −8 ≤ 𝑥 ≤ 8

• −9 ≤ 𝑥 ≤ 7

• −4 ≤ 𝑥 ≤ 12

• −2 ≤ 𝑥 ≤ 2