7 Section 1.8 Transformations of Functions
a. [latex]g(x)=f(x-2)+1[/latex]
b. [latex]h(x)=\frac{1}{2}f(x)-2[/latex]
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Answers
a. To make [latex]g(x)[/latex], [latex]f(x)[/latex] has been shifted right 2 units, and up 1.
b. To make [latex]h(x)[/latex], [latex]f(x)[/latex] has been vertically compressed by [latex]\frac{1}{2}[/latex] and shifted down 2.
2. Given the parent function [latex]g(x)=\sqrt{x}[/latex], write the equations of each child function described below.
a. Child function [latex]h(x)[/latex] is [latex]g(x)[/latex] that has been shifted left 3 units, reflected across the [latex]x[/latex]-axis and shifted up 4 units.
b. Child function [latex]k(x)[/latex] is [latex]g(x)[/latex] that has been reflected across the [latex]y[/latex]-axis, and vertically stretched by 5.
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Answers
a. [latex]h(x)=-\sqrt{x+3}+4[/latex]
b. [latex]k(x)=5\sqrt{-x}[/latex]