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Math  /  Algebra

QuestionDescribe the transformations of the parent function f(x)=∣x∣f(x)=|x|
1. g(x)=−∣x∣+5g(x)=-|x|+5

Studdy Solution

STEP 1

1. The parent function is f(x)=∣x∣ f(x) = |x| , which is the absolute value function.
2. Transformations include vertical shifts, vertical reflections, and vertical stretches/compressions.

STEP 2

1. Identify the vertical reflection.
2. Identify the vertical shift.

STEP 3

Identify the vertical reflection:
The function g(x)=−∣x∣+5 g(x) = -|x| + 5 includes a negative sign in front of the absolute value, −∣x∣ -|x| . This indicates a vertical reflection across the x-axis. The graph of f(x)=∣x∣ f(x) = |x| is flipped upside down.

STEP 4

Identify the vertical shift:
The function g(x)=−∣x∣+5 g(x) = -|x| + 5 includes a "+5" outside the absolute value. This indicates a vertical shift upwards by 5 units. The entire graph is moved up by 5 units.
The transformations of the parent function f(x)=∣x∣ f(x) = |x| to obtain g(x)=−∣x∣+5 g(x) = -|x| + 5 are:
1. A vertical reflection across the x-axis.
2. A vertical shift upwards by 5 units.

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