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

Answer:

  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

Step-by-step 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.

  $y=\left|\dfrac{x}{2}-2\right|+3+1\\\\\boxed{y=\left|\dfrac{x}{2}-2\right|+4}$

b) one unit down

Subtract 1 from the function value.

  $y=\left|\dfrac{x}{2}-2\right|+3-1\\\\\boxed{y=\left|\dfrac{x}{2}-2\right|+2}$

c) one unit left

Replace x with x-(-1).

  $y=\left|\dfrac{x-(-1)}{2}-2\right|+3\\\\\boxed{y=\left|\dfrac{x+1}{2}-2\right|+3}$

d) one unit right

Replace x with x-1.

  $\boxed{y=\left|\dfrac{x-1}{2}-2\right|+3}$