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y=x+ abs x+1 abs

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2 Answers

Look Dan, Robert in CA gave you an answer; I hope that helps.

But the stump for you was that your calculator graphed it and you did not understand the steps, right?

the given function was y = x + |x+1|

you should know that if x+1 is >= o, then the function is y = x + (x+1) = 2x+1, but if x+1 < 0 [ x < -1],

then the function is  y = x + -(x+i) = -1 or a flat line down there...

That is wat you device did, in milliseconds = graph a flat line to x=-1

and then a rising line with slope 2 after that. Get it? Got it? Good!

I am interpreting yoru question as:

y = x + | x + 1|

The absolute value of a number is either the number or its opposite, whichever is positive.

For x < 0, |x| = -x. For x ≥ 0, |x| = x

Examples:

|-2| = -(-2) = 2

|7| = 7

For your equation, you have |x+1|. When x + 1 < 0, |x+1| = -(x+1) = -x-1. When x+1 ≥ 0, |x+1| = x+1.

x+1 ≥ 0 is the same as saying x ≥ -1.

x + 1 < 0 is the same as saying x  < -1

So your equation could be described as two separate equations depending on what the vlaue of x is:

y = x + | x + 1|

For x < -1:

y = x + -(x+1)

or y = -1

For x ≥ -1:

y = x + x +1

or y = 2x + 1

To summarize:

y = -1 {x < -1} and y = 2x + 1 {x ≥ -1}

This is called a piecewise function since it is defined in pieces. All functions with absolute values can be turned into piecewise functions.

This graph should look like a steep upward climbing line to the right of x = -1 and a horizontal line below the y axis to the left of x = -1. At x = -1, the y value is -1 for both halves of the equation, so it is a continuous function.

I'm not sure where the question wants you to go with this since you are not given any y or x values to plug in and use to solve. Perhaps there is more to the problem you can add with the discussion feature.

 

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