41.3k views
3 votes
Describe the transformations that occur to the function f(x) = |x| in the proper order to produce the function

g(x)=|x+2| -7

User MayurK
by
7.7k points

1 Answer

1 vote

The function f(x) = |x| transforms into g(x) = |x + 2| - 7 through a leftward shift by 2 units, a potential reflection, and a downward shift by 7 units, altering its position and shape.

To transform the function f(x) = |x| into g(x) = |x + 2| - 7, several key transformations occur in a specific order.

Translation Left:

The term x + 2 inside the absolute value function implies a horizontal shift to the left by 2 units, changing the position of the "peak" of the absolute value graph.

Reflection (if needed):

Since f(x) = |x| is already symmetric about the y-axis, no reflection is required. However, if the original function were f(x) = x^2, for example, a reflection would be necessary.

Vertical Shift Down:

The constant term -7 outside the absolute value affects the entire graph by vertically shifting it downward by 7 units.

Combining these transformations, the sequence is as follows:

g(x) = |x + 2| - 7

This transformation sequence ensures that the graph retains the V-shape characteristic of the absolute value function but shifts left, possibly reflects, and then shifts downward.

User Rajesh Yogeshwar
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.