Question

Describe two different ways to use transformations to change f(x) = x into g(x)=-3x-12

Answer 1

See below

Explanation:

Given

• Function f(x) = x

Transformation ways

1. Reflection by a factor of (-3) and vertical shift down -12 units

• f(x) = x → (-3) ⇒ h(x) = -3x → (-12) ⇒ g(x) = -3x - 12

2. Vertical shift up by 4 units and reflection by a factor of (-3)

• f(x) = x → (+4) ⇒ h(x) = x + 4 → (-3) ⇒ g(x) = -3x - 12