Question

write the equation for each translation of the graph of y=| 1/2x-2|+3
One unit up
one unit down

Answer 1

Answer:

y=|1/2x-2|+4

y=|1/2x-2|+2

Step-by-step explanation:

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Answer 2

The equation for each translation of the graph of y=| 1/2x-2|+3 is

g(x)=| 1/2x-3/2|+3.

Given that,

$y=| 1/2x-2|+3$

Translate the above one unit to the left

Replace y with f(x)

$f(x)=| 1/2x-2|+3$

What is the meaning of translation?

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

When an absolute function is translated to the left, the resulting function is,

$g(x)=f(x-h)$

Because it is been translated 1 unit to the left, h = -1

$g(x)=f(x-(-1))$

$g(x)=f(x+1)$

Now we calculate f(x+1)

$f(x+1)=| 1/2(x+1)-2|+3$

$f(x+1)=| 1/2x+1/2-2|+3\\f(x+1)=| 1/2x+1-4/2|+3$

$f(x+1)=| 1/2x+(-3)/2|+3\\\\f(x+1)=| 1/2x-3/2|+3$

We have,g(x)=f(x+1)

$g(x)=| 1/2x-3/2|+3$

To learn more about the translation visit:

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