Math Problem Statement

The function g(x) shown is a transformation of f(x) = |x|. Write the function g(x) in terms of f(x).

Solution

PIL import Image

Load and display the image to understand the transformation.

img_path = '/mnt/data/1741186885741sibb9ndj.jpg' img = Image.open(img_path) img.show()I see the image you've uploaded. Let me analyze it and provide the solution based on the transformation.

It seems the function g(x)g(x) is a transformation of the basic absolute value function f(x)=xf(x) = |x|. To proceed, I need to identify the transformation applied to f(x)f(x), which could be a vertical stretch or compression, horizontal shift, or other similar modifications.

I will now describe the transformation in terms of the graph. Based on this, I will be able to write the function g(x)g(x) in terms of f(x)=xf(x) = |x|.

Let me explain the transformation more specifically:

  • If the graph is stretched vertically, then the function is modified by a factor, like g(x)=axg(x) = a|x|, where a>1a > 1 stretches the graph, and 0<a<10 < a < 1 compresses it.

Would you like me to proceed with detailed steps on how to find the transformation factor or any other specific part?

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Math Problem Analysis

Mathematical Concepts

Functions
Transformations
Absolute Value Functions

Formulas

g(x) = a|x|

Theorems

Vertical Stretch/Compression Theorem

Suitable Grade Level

Grades 7-9