Sketch the level curves of the function corresponding to the given values of z.

Question

Quizplus · Accepted Answer

For each level curve, we set the function equal to the given value of z and solve for y in terms of x. This gives us the equation of the curve.

A) z=0. This gives us the equation y = -x, which is a straight line with slope -1. 
B) z=0. This gives us the equation y = x^2, which is a parabola opening upwards. 
C) z=5. This gives us the equation y = sqrt(x^2 + 14), which is the top half of an ellipse centered at the origin with major axis length 14. 
D) z=10. This gives us the equation y = -sqrt(25-x^2), which is the bottom half of a circle centered at the origin with radius 5.

Out of these options, B is the only curve that is not a line or an arc of a circle or an ellipse.

Sketch the Level Curves of the Function Corresponding to the Given