Question

What is the function g(x) that results when translating the function f(x) = |x| to the left 12 units and reflecting it over the x-axis?

Answer 1

Answer: Translation up 5 units means g(x)=f(x)+5g(x)=f(x)+5. Reflecting this across the x-axis means g(x)=-(f(x)+5)g(x)=−(f(x)+5).

-(4x+5)=-4x-5

−(4x+5)=−4x−5

Explanation:

Answer 2

g(x) = -|x + 12|

Explanation:

Translation to left ≡ f(x + 12)

f(x + 12) = | x + 12 |

Reflection of a function f(x) about the x - axis is keeping the x value same but negating the y values

Reflected f'(x) = -y = -f(x)

Taken together

g(x) = -(|x + 12|)