The function  g(x)
graphed in blue (solid) below is obtained by shifting the graph of  f(x)
in red (dashed) vertically and horizontally.

Maple plot

The formula for  g(x)
is

g(x)=

To express the formula for \( g(x) \), we need to analyze the shifts that were applied to the function \( f(x) \) to obtain \( g(x) \). Since

The function g(x) graphed in blue (solid) below is obtained by shifting the graph of f(x) in red (dashed) vertically and horizontally. The formula for g(x) is?

Understand how to find the formula for g(x) by applying vertical and horizontal shifts to the graph of f(x). This problem explores function transformations, key concepts in graph shifting, and the formula g(x) = f(x - h) + k. Suitable for high school students in Grades 10-12.

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