Question

What is the effect on the graph of the linear parent function, f(x) = x, when f(x) is replaced by f(x + 5)?

A) The graph of the line becomes steeper.
B) The graph of the line shifts horizontally right 5 units.
C) The graph of the line shifts vertically down 5 units.
D) The graph of the line shifts horizontally left 5 units.

Answer 1

Here are the rules:
F(x + a) shifts a units left.
F(x - a) shifts a units right.

You can see this by taking for example f(x) = x^2 then f(x+5) = (x+5)^2, if you graph y=x^2 and y=(x+5)^2, you will see it is shifted 5 units to the right.

Answer 2

D) The graph of the line shifts horizontally left 5 units.

Adding a number, n, inside of the parenthesis with x would move the parent function n units to the left.