Question

F(x) = x2 + 5x – 1 is shifted 3 units left. The result is g(x). What is g(x)?

A. g(x) = (x – 3)2 + 5(x – 3) – 1
B. g(x) = x2 + 5x + 2
C. g(x) = (x + 3)2 + 5x – 1
D. g(x) = (x + 3)2 + 5(x + 3) – 1

Answer 1

D. When you shift left you add the units to all x because the x is what shifts. Even though you moved left, it is positive. If you move right , it is minus.

Answer 2

g(x) = (x+3)² + 5(x+3) – 1.

Explanation:

Given : f(x) = x² + 5x – 1 is shifted 3 units left.

To find : The result is g(x). What is g(x).

Solution : We have given that

f(x) = x² + 5x – 1 is shifted 3 units left.

By the transformation rule : If f(x) →→ f(x +h) shifted by h unit left .

f(x) = x² + 5x – 1 is shifted 3 units left.

Here , h = 3

Then g(x) = (x+3)² + 5(x+3) – 1.

Therefore, g(x) = (x+3)² + 5(x+3) – 1.