Question

Write the equation of a function whose parent function, f(x) = x + 5, is shifted 3 units to the right.

g(x) = x + 3
g(x) = x + 8
g(x) = x − 8
g(x) = x + 2

Answer 1

The equation of the function that results from shifting the parent function f(x) = x + 5 by 3 units to the right is g(x) = x + 2.

Step-by-step explanation:

To find the equation of a function that is shifted 3 units to the right of the parent function f(x) = x + 5, we can use the concept of horizontal shifts in functions. A function f(x - d) represents a shift to the right by d units. In this case, we want to shift f(x) by 3 units to the right, so we substitute x with (x - 3).

Therefore, the function after shifting 3 units to the right is:
g(x) = (x - 3) + 5 = x + 2.

Answer 2

Option D

The equation of a function whose parent function, f(x) = x + 5, is shifted 3 units to the right is g(x) = x + 2

Solution:

Given that, f(x) = x + 5 is shifted 3 units to the right

If the function f(x) translated horizontally to the right by h units, then the new function g(x) = f(x - h)

If the function f(x) translated horizontally to the left by h units, then the new function g(x) = f(x + h)

f(x) = x + 5 is shifted 3 units to the right:

The new function, g(x) = f(x - h)

Here "h" = 3

f(x) = x + 5

The x in f(x) will change to (x - 3)

The new function = (x - 3) + 5

The new function = x + 2

Thus g(x) = x + 2

Option D is correct