Question

6. Consider the following function. f(x) = x2 - 4. Part A: Write a function that shifts f(x) left 5 units. Part B: Write a function that shifts f(x) right 8 units. Part C: Write a function that horizontally stretches f(x) by units. 1 Part D: Write a function that horizontally compresses f(x) by 6 units. Part E: Write a function that reflects f(x) about the x -axis.

Answer 1

We are given the following function

`f(x)=x^2-4`

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

`f(x)\rightarrow f(x+b)`

Let us apply the above rule

`f(x)=(x+5)^2-4`

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

`f(x)\rightarrow f(x-b)`

Let us apply the above rule

`f(x)=(x-5)^2-4`

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

`f(x)\rightarrow f(bx)`

Let us apply the above rule

`\begin{gathered} f(x)=(1\cdot x^2)-4 \\ f(x)=x^2-4 \end{gathered}`

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.

`f(x)\rightarrow f(bx)`

Let us apply the above rule

`\begin{gathered} f(x)=(6\cdot x^2)-4 \\ f(x)=6x^2-4 \end{gathered}`

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

`f(x)\rightarrow-f(x)`

Let us apply the above rule

`\begin{gathered} f(x)=-(x^2-4) \\ f(x)=-x^2+4 \end{gathered}`