Sketch the curves y =|x| and y = 2 - x^2 on the graphs

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SUMMARY

The discussion focuses on sketching the graphs of the functions y = |x| and y = 2 - x^2. The curve y = |x| is represented as two linear segments at 45 degrees to the x-axis, while y = 2 - x^2 is an inverted parabola with its vertex at (0, 2). The main inquiry is to determine the values of x for which the inequality |x| < 2 - x^2 holds true, which involves finding the points of intersection between the two graphs. The solution requires setting |x| equal to 2 - x^2 and solving for x in both positive and negative domains.

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Homework Statement


Sketch on the same axis the graphs of y = |x| and y = 2 - x^2.

For which values f x is the inequality |x| < 2 - x^2


Homework Equations





The Attempt at a Solution



I don't really understand what it is asking me to do, I've sketched the two curves, y = |x| 45 degrees from the x-axis and at -45 degrees from the x axis, and the curve y = 2 - x^2 is an upside down quadratic curve with the vertex at -2 y.

thanks
 
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for which values of x is the graph of y = |x| under the graph of y = 2 - x^2 ?
 
is that what its asking?

if so how do i work that out, is it similar to the wa you work out whether a curve crosses the x-axis.

thanks
 
you first draw graphs, then find the points of intersection for the relevant places.
 
ok, but how?? :S
 
if you have drawn the graphs you just plug in |x| in the y = 2 - x^2

so we get:

x = 2 - x^2, for x > 0

and

-x = 2 - x^2, for x < 0

points of intersection is where the two graphs/functions are equal...
 
Last edited:

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