Question

I'm in desperate need of help on how to do these 4 problems.

Write the function g(x) with the indicated transformations.

1. f(x)=x; translated right 3 units

2. f(x)=x^2; vertical stretch by 5, translated down 3 units and reflected across the x-axis

3 f(x)=|x|; vertical shrink by 1/4, and right 1 unit and up 2 units

4. f(x)=-(x-4)^2; vertical stretch by a factor of 3, translated up 2 and right 8

Answer 1

#1 g(x) = f(x-3) = x-3

#2 g(x):
stretch y by 5: 5f(x)
down 3: 5f(x)-3
x reflect: -(5f(x)-3) = 3 - 5f(x)
g(x) = 3 - 5x^2

#3 g(x):
shrink y by 4: (1/4)f(x)
right 1: (1/4)f(x-1)
up 2: (1/4)f(x-1)+2
g(x) = (1/4)|x-1|+2

#4 g(x):
y stretch 3: 3f(x)
up 2: 3f(x)+2
right 8: 3f(x-8)+2
g(x) = 3[-((x-8)-4)^2)]+2 = 2-3(x-12)^2