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
[tex]\begin{gathered} when \\ g(x)=x+7 \end{gathered}[/tex]
Thus, we will have
[tex]shifting\text{ to the left by 7 units}[/tex]
For part B
when
[tex]g(x)=x-5[/tex]
The translation here is
[tex]A\text{ shifting to the right by 5 units}[/tex]
Part C
For the function
[tex]g(x)=(x+2)[/tex]
The graph is
Thus, we have the translation as A horizontal shift to the left by 2 units
Part D
The given function is
[tex]g(x)=(x-7.5)[/tex]
The transformed graph is
The translation is a shift to the right by 7.5 units
