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Please give the step-by-step solution with detailed explanation. 1.) The function g is related to one of the parent functions g(x) = x^2 + 6 The parent function f is: f(x)= x^2 Use function notation to write g in terms of f. 2.) The function g is related to one of the parent functions g(x) = x2 – 3 The parent function is: f(x)= x^2 Use function notation to write g in terms of f. 3.) The function g is related to one of the parent functions g(x) = −(x − 2)^3 a.) Identify the parent function f. b.) Use function notation to write g in terms of f. 4.) The function g is related to one of the parent functions g(x) = |x − 1| + 5 a.) Identify the parent function f. b.) Use function notation to write g in terms of f. 5.) The function g is related to one of the parent functions g(x) = 2 √x a.) Identify the parent function f. b.) Use function notation to write g in terms of f.

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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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