Question

Option 1: Explain in your own words the difference between the domain of a function and the range of a function. Provide an example for explaining how to find domain of an equation (use equation editor). Provide a visual example of a graph using the "insert image" feature and explain how to find the domain and range from the graph. Last, present a problem for your peers so they may practice identifying domain and range. Make sure to check on them to tell them if they are correct. If no one attempts your problem, post the solution on Sunday

Answer 1

Domain is the set of values over which the function is defined aka the values it can take as input

Range is the set of values which the function outputs

To find the domain of a function say we first need to know about the square root function

Va2-22

Namely we need to know that the square root function is defined only for non-negative real numbers

So the domain is defined by the constraint

2

We can now solve this as

(x2)0 x < 0 or x 2

So the domain is

E (O0, 0 U 2, o0)

For the range, we note that the square root of any number (Where defined) is always positive. So the range is

0, oo)

Graph is below:

40 + 662 213 30 101 30 = 21.380952381 X -2x 20 10 30 мо 20 10 20 30 powered by desmos

Graphically, we find that the value of the function is always above the X-axis confirming our range as

0, oo)

And that there is a small gap where the function is undefined. This is the gap confirming our domain as
E (O0, 0 U 2, o0)

Problem:
arccos
has domain
TE (0,-1U 1, oo)
and range
0, T