Horizontal Function Shifts

The graph of a function is shifted horizontally by a if you replace x by “x – a”.

What is the formula of the function with the given horizontal shift?

1. The function g(x) is obtained from f(x) = |x| by shifting to the right 5 units.

What is the formula for g(x)?

2. g(x) is obtained from f(x) = x^{3} by shifting to the left 1 unit.

What is the formula for g(x)?

3. g(x) is obtained from f(x) = x^{2} – 7x + 1 by shifting to the right 3 units.

What is the formula for g(x)?

4. g(x) is obtained from f(x) = (x – 10)^{4} + 9 by shifting to the left 2 units.

What is the formula for g(x)?

5. g(x) is obtained from f(x) = |x – 3| + x by shifting to the right by 1 unit.

What is the formula for g(x)?