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

[uniidiot]

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

 

[malawi_glenn]

for which values of x is the graph of y = |x| under the graph of y = 2 - x^2 ?

 

[uniidiot]

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

 

[malawi_glenn]

you first draw graphs, then find the points of intersection for the relevant places.

 

[uniidiot]

ok, but how?? :S

 

[malawi_glenn]

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...