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

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Homework Help Overview

The problem involves sketching the graphs of the functions y = |x| and y = 2 - x^2 on the same axis and determining the values of x for which the inequality |x| < 2 - x^2 holds true.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the shapes of the curves and their intersections, with some questioning how to determine the values of x where one graph is below the other.

Discussion Status

Participants are actively exploring the problem, with some suggesting methods to find points of intersection after sketching the graphs. There is a lack of explicit consensus on the approach, but guidance on drawing the graphs and finding intersections has been provided.

Contextual Notes

Participants express uncertainty about the problem's requirements and the methods to solve it, indicating a need for clarification on the relationship between the two functions.

uniidiot
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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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