Question

Explain how to find the domain and range of a rational function from its graph

Answer 1

Domain

Any vertical asyptotes?

Range

A little trickier. There may be an horizontal asymptote for one piece of the Domain, but that doesn't necessarily mean it is NOT in the Range.

Answer 2

it wants me to explain how to do it with out quoting the book.

Answer 3

Okay, let's see you spell it out. Generally, start with All Real Numbers and see if you can you rule out anything.

Answer 4

The way i learnt, domain = values of x.
range = values of y?

Answer 5

Let's establish one thing. What does it mean by "its graph"? All we have is a pretty picture?

Answer 6

Its a two part quest, #1 explain how to do it then #2 do it by using a graph supplied. horizontal asymptope=2 and veritical asymptote = -2 and 2

Answer 7

An equation will be a function if for any x in the domain of the equation (the domain is all the x’s that can be plugged into the equation) the equation will yield exactly one value of y.
Domain of a function is the set of all values that can be plugged into a function and have the function exist and have a REAL NUMBER for a value.
So, for the domain we need to avoid division by zero, square roots of negative numbers, logarithms of zero and logarithms of negative numbers.
The range of a function is simply the set of all possible values that a function can take.

Answer 8

it is the same for a rational function?

Answer 9

See problem K in attachment

Answer 10

It's the same for everything. It is a fundamental definition.

"#1 explain how to do it then #2 do it by using a graph supplied. horizontal asymptope=2 and veritical asymptote = -2 and 2"

Domain is easy. All Real Numbers except x = 2 and x -2 -- Done.
Range is a little trickier. We need to know what it does between x = 2 and x = -2. Does the graph take on the value y = 2 in there?

Answer 11

Clearly from the drawing, the graph never takes on y = 2. There is also a bit of a space between about y = 0.4 and y = 2. That's not in the Domain, either.

Answer 12

Unfortunately, without the actual equation, it is not possible to determine the EXACT value of the bottom of that interval. It just isn't labled.

Answer 13

@tkhunny second part of the problem poses a problem since it not labeled. So Domain, All Real Numbers except x = 2 and x -2 right

Answer 14

Right. Range is All Real Numbers except (something,2)