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Mekhanik [1.2K]
3 years ago
7

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.
Mathematics
1 answer:
alukav5142 [94]3 years ago
7 0

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

<u>a) one unit up</u>

Add 1 to the function value.

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

<u>b) one unit down</u>

Subtract 1 from the function value.

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

<u>c) one unit left</u>

Replace x with x-(-1).

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

<u>d) one unit right</u>

Replace x with x-1.

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

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