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1. The function [tex]g(x)=x^2+6[/tex] is related to the parent function[tex]f(x) = x^2[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply add 6 to the expression for
[tex]f: g(x) = f(x) + 6\\ = x^2 + 6[/tex]
2. The function [tex]g(x) = x^2 - 3[/tex] is related to the parent function [tex]f(x) = x^2[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply subtract 3 from the expression for
[tex]f: g(x) = f(x) -3 \\ = x^2 -3[/tex]
3.The function [tex]g(x) = -(x -2)^3[/tex] is related to the parent function [tex]f(x) = (x - 2)^3[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply negate the expression for f:
[tex]g(x) = -f(x)\\= -(x - 2)^3[/tex]
4. The function [tex]g(x) = |x -1| + 5[/tex] is related to the parent function [tex]f(x) = |x - 1|[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply add 5 to the expression for f:
[tex]g(x) = f(x) + 5\\= |x - 1| + 5[/tex]
5. The function [tex]g(x) = 2 \sqrt{x}[/tex] is related to the parent function [tex]f(x) = \sqrt{x}[/tex]. To write [tex]g[/tex] in terms of [tex]f[/tex], you can simply multiply the expression for f by 2:
[tex]g(x) = 2[/tex] × [tex]f(x)[/tex]
[tex]= 2 \sqrt{x}[/tex]
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