Question

Find g(x), where g(x) is the translation 5 units up of f(x)=x.

A) g(x) = x + 5
B) g(x) = x - 5
C) g(x) = x + 10
D) g(x) = x - 10

Answer 1

To translate the function f(x) = x by 5 units up, add 5 to the function resulting in g(x) = x + 5. This represents the new function with all y-values increased by 5. Therefore, Option A is correct.

Step-by-step explanation:

To translate the function f(x) = x by 5 units up, we need to add 5 to the entire function. This is because when we say translating a graph up or down, we are referring to the y-values on the graph. Thus, every y-value of the function will be increased by 5 units, which means we add 5 to the original function f(x).

The new function, g(x), will look like f(x) with every point moved 5 units higher on the y-axis. Therefore, the translated function g(x) = x + 5 represents the original function moved up by 5 units.

Option A is the correct choice because it shows the addition of 5 to the original function f(x), resulting in the translated function being g(x) = x + 5.