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Sagot :
We are given the following function
[tex]f(x)=x^2-4[/tex]Let us perform the transformations on the above function.
Part A: Write a function that shifts f(x) left 5 units
The following rule is used to shift f(x) left by b units
[tex]f(x)\rightarrow f(x+b)[/tex]Let us apply the above rule
[tex]f(x)=(x+5)^2-4[/tex]Part B: Write a function that shifts f(x) right 8 units
The following rule is used to shift f(x) right by b units
[tex]f(x)\rightarrow f(x-b)[/tex]Let us apply the above rule
[tex]f(x)=(x-5)^2-4[/tex]Part C: Write a function that horizontally stretches f(x) by 1 unit
The following rule is used to horizontally stretch the f(x) by b units
[tex]f(x)\rightarrow f(bx)[/tex]Let us apply the above rule
[tex]\begin{gathered} f(x)=(1\cdot x^2)-4 \\ f(x)=x^2-4 \end{gathered}[/tex]Part D: Write a function that horizontally compresses f(x) by 6 units.
The following rule is used to horizontally compress the f(x) by b units.
[tex]f(x)\rightarrow f(bx)[/tex]Let us apply the above rule
[tex]\begin{gathered} f(x)=(6\cdot x^2)-4 \\ f(x)=6x^2-4 \end{gathered}[/tex]Part E: Write a function that reflects f(x) about the x-axis.
The following rule is used to reflect f(x) about the x-axis
[tex]f(x)\rightarrow-f(x)[/tex]Let us apply the above rule
[tex]\begin{gathered} f(x)=-(x^2-4) \\ f(x)=-x^2+4 \end{gathered}[/tex]
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