X=|y| what is the domain and range ?

Mathematics

1 answer:

cricket20 [7]3 years ago

5 0

Answer:

Domain: x ≥ 0

Range: All real numbers

Step-by-step explanation:

This is an absolute value function which creates a V for its graph. Since the absolute value is on y, the function is rotated to the right or sideways.

This means only the x values of 0 and greater are used in the function. Since the domain is the set of all x values then it is x≥0.

This also means that all y values are used on the y-axis. There is no restriction on the y values. Since the range is the set of all y values then it is all real numbers.

You might be interested in

Evaluate the surface integral. S xz ds, s is the part of the plane 2x 2y z = 4 that lies in the first octant

maksim [4K]

The value of the given surface integral is 4.

The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.

$S(u,v)=(1-u)((1-u)(2,0,0)+u(0,2,0)+u(4,0,0)\\S(u,v)=(2(1-u)(1-v),2u(1-v),4v)$

<h3>What is the surface integral?</h3>

A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.

with 0≤u≤1 and 0≤v≤1. Then the surface element ds is equivalent to

$ds=\||\:\left(s_u\times \:\:S_v\right)||dudv=12\left(1-v\right)dudv$