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Y = |x - 5| + |x + 5| if x >5

User Hamilton
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1 Answer

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Answer:

y = 2x

Explanation:

You want the simplified form of y = |x -5| +|x +5| if x > 5.

Turning points

The graph of the whole function will have turning points where the absolute value expressions are 0:

x -5 = 0 ⇒ x = 5

x +5 = 0 ⇒ x = -5

For values of x > 5, we are concerned with that portion of the graph that is to the right of both of these turning points. Hence, both absolute value expressions are positive and unchanged by the absolute value bars.

y = (x -5) +(x +5) . . . . . . if x > 5

y = 2x . . . . . . . . . . . . . . collect terms

The simplified function is y = 2x.

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Additional comment

The attached graph shows y=2x and the given function for x > 5. They are identical. (The y=2x graph is shown dotted, so you can see the red graph of the given function.)

Y = |x - 5| + |x + 5| if x >5-example-1
User Bruvio
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