Question

Describe the translation in each function as it relates to the graph of f(x) = x.g(x)=x+7g(x)=x-5g(x) = (x + 2)g(x)=(x-7.5)

Answer 1

Step-by-step explanation

We are asked to describe the translation of the functions with respect to f(x) =x

To translate the function up and down, you simply add or subtract numbers from the whole function. If you add a positive number (or subtract a negative number), you translate the function up. If you subtract a positive number (or add a negative number), you translate the function down.

In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.

To do so, we will have to plot the graph of each function and compare it with f(x) represented by the red lines below

Part A

`\begin{gathered} when \\ g(x)=x+7 \end{gathered}`

Thus, we will have

`shifting\text{ to the left by 7 units}`

For part B

when

`g(x)=x-5`

The translation here is

`A\text{ shifting to the right by 5 units}`

Part C

For the function

`g(x)=(x+2)`

The graph is

Thus, we have the translation as A horizontal shift to the left by 2 units

Part D

The given function is

`g(x)=(x-7.5)`

The transformed graph is

The translation is a shift to the right by 7.5 units