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Describing Transformations of Linear Functions

Describing Transformations of Linear Functions 1.2 - Solution

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We are given the graphs of f(x)f(x) and g(x)g(x) on a coordinate plane, and want to describe the transformation from the graph of f(x)f(x) to the graph of g(x).g(x). Let's find some corresponding points in the graphs and measure the distance between them.

We see that the graph of g(x)g(x) is a horizontal translation 22 units left of the graph of f(x).f(x). We can also see this using the function rules. The function g(x)g(x) can be written on the form y=f(xh).y=f(x-h). g(x)=f(x+2)g(x)=f(x(-2)) g(x)=f(x+2) \quad \Leftrightarrow \quad g(x)=f(x-(\text{-} 2)) In our function, we have that h=-2.h=\text{-} 2. This means the graph of g(x)g(x) is a horizontal translation 22 units left of the graph of f(x).f(x).