Question

Write the expression for the function whose graph is the graph of y = x^3 but shifted down 4 units and left 5 units.

A.
y = (x - 5)^3 - 4

B.
y = (x + 5)^3 - 4

C.
y = (x - 5)^3 + 4

D.
y = (x - 4)^3 - 5

Answer 1

1. Consider y=f(x)

2. let a and b be 2 positive numbers

3. then the graph of y=f(x)-a is the graph of y=f(x) shifted a units down

4. the graph of y=f(x+b) is y=f(x) shifted b units left
y=f(x-b) is y=f(x) shifted b units right

5. y=f(x+b)-a is the graph of y=f(x) shifted a units down and b units left

6. So
`y=x^(3)` shifted 4 units down and 5 units left is the graph of


`y=(x+5)^(3)-4`

7. To check: consider
`y=x^(3)` at x=3. We have the point (3, 27)

Shift this point 4 units down and 5 units left: (3-5, 27-4)=(-2, 23)

Consider
`y=(x+5)^(3)-4` for x=-2


`(-2+5)^(3)-4=(3)^(3)-4=27-4=23`