Question

Write the expression for when you translate the graph of y = | 1/2 x−2 |+3 a) one unit up, b) one unit down, c) one unit to the left, d) one unit to the right.

Answer 1

a) y = |x/2 -2| +4

b) y = |x/2 -2| +2

c) y = |(x+1)/2 -2| +3

d) y = |(x-1)/2 -2| +3

Explanation:

To translate the function f(x) by (h, k) in the (right, up) direction, you transform it to ...

g(x) = f(x -h) +k

a) one unit up

Add 1 to the function value.

`y=\left|(x)/(2)-2\right|+3+1\\\\\boxedy=\left`

b) one unit down

Subtract 1 from the function value.

`y=\left|(x)/(2)-2\right|+3-1\\\\\boxedy=\left`

c) one unit left

Replace x with x-(-1).

`y=\left|(x-(-1))/(2)-2\right|+3\\\\\boxed(x+1)/(2)-2\right`

d) one unit right

Replace x with x-1.

`\boxedy=\left`