graph solution set x<=y2 y>=x

Question

graph the following solution set x<=y2  y>=x

Answer 1

graph solution set
x <= y^2
y >= x

x = y^2 is a horizontal parabola with vertex (0,0) opening to the right.
So x <= y^2 means all points on the parabola and to the left.

y = x is a line through the origin with slope 1.
y >= x are all points on and above the line.

The line and the parabola intersect when x = x^2,
or x(x-1) = 0, i.e., x = 0 or 1.

The part of the parabola that comes into play is just that part above y = x; that’s y = sqrt(x) on interval [0,1].

So the solution set will be all points on or above sqrt(x) on the interval [0,1] and on or above the line otherwise.

See GeoGebra sketch here:
http://www.wyzant.com/resources/files/262542/region_solution_set

Answer 2

Hi Helen;

y≥x

The line will be a solid, non-dotted line to highlight the fact that y=x.  (We will address y>x below.)  Otherwise, this will be treated as any other linear equation...

y=mx+b

The slope, change-of-y divided by change-of-x, also known as rise-over-run, of the line is 1.

The y-intercept, value of y when x=0, is 0, (0,0).

For graphing, you will begin your line at (0,0).  Your line will rise 1 unit as it runs to the right 1 unit.  As your line decreases 1 unit, it will run 1 unit to the left.  You will then shade the area to the left of this line to highlight the fact that y>x.

x≤y²

This is a parabola.  Because it is the y which has two values for every value of x, the parabola opens sideways.  Because the value of y² is positive, it opens to the right.  The vertex is (0,0).

  It will be a solid line to highlight the fact that x=y².  As per Steve's answer, the area to the left will be shaded to highlight the fact that y²>x.