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.

a) y = |½x − 2| + 4;         b) y = |½x − 2| + 2;

c) y = (|½(x + 1) − 2| + 3; d) y = ( |½(x - 1) −2| + 3

Step-by-step explanation:

a) One unit up

To translate a function one unit up, you add one unit to y.

y = |½x − 2| + 3  + 1 = |½x − 2| + 4

b) One unit down

To translate a function one unit down, you subtract one unit from y.

y = |½x − 2| + 3  - 1 = |½x − 2| + 2

c) One unit to the left

To translate a function one unit to the left, you add one unit to x.

y = |½(x + 1) −2| + 3 = (|½(x + 1) − 2| + 3

d) One unit to the right

To translate a function one unit to the right, you subtract one unit from x.

y = |½(x + 1) −2| + 3 = (|½(x - 1) −2| + 3

The first diagram below shows the function shifted one unit up and down, and the second shows your function shifted one unit left and right.