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.

maybe showing the graph would

step-by-step explanation:

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