# Calc 3 Range of a function (set of points)

• xtrubambinoxpr
In summary, the conversation discusses a problem with inequalities and how to solve it. The person provides an image and equations for reference and asks for help understanding the steps taken. Another person explains that the inequalities were flipped and then the whole line was flipped to solve the problem.
xtrubambinoxpr

## Homework Statement

See attached image

## Homework Equations

they are provided in the image. I see the domain is used

## The Attempt at a Solution

I can't figure out how they went from step one to step 2. where does the -81 come from and the 9 multiplied to the function in the middle. I tried to figure it out and all i got was divide everything by 9 then multiplying by 18 across to get 9 in the middle but that won't get me 81 on the eft hand side.

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xtrubambinoxpr said:

## Homework Statement

See attached image

## Homework Equations

they are provided in the image. I see the domain is used

## The Attempt at a Solution

I can't figure out how they went from step one to step 2. where does the -81 come from and the 9 multiplied to the function in the middle. I tried to figure it out and all i got was divide everything by 9 then multiplying by 18 across to get 9 in the middle but that won't get me 81 on the eft hand side.

What happens to the first batch of inequalities when you multiply everything by -9?

gopher_p said:
What happens to the first batch of inequalities when you multiply everything by -9?
Well I'm pretty retarded lol
But what about the greater than or equal to signs? And why weren't they reversed? Like from elementary you learn to flip them if it's anything with a negative number.

xtrubambinoxpr said:
Well I'm pretty retarded lol

I doubt that very much if you're taking Calc 3. Inexperienced? Almost definitely. Ill prepared? Possibly. Too stupid? Not very likely.

But what about the greater than or equal to signs? And why weren't they reversed? Like from elementary you learn to flip them if it's anything with a negative number.

Look again. The inequalities were flipped, and then the whole line was flipped.

gopher_p said:
I doubt that very much if you're taking Calc 3. Inexperienced? Almost definitely. Ill prepared? Possibly. Too stupid? Not very likely.

Look again. The inequalities were flipped, and then the whole line was flipped.
Ahhhhh I see it now! Thanks a lot! This helps a lot this section because I couldn't put the pieces together!

## 1. What is the definition of the range of a function?

The range of a function is the set of all possible output values, or dependent variables, that the function can produce for a given set of input values, or independent variables.

## 2. How do you find the range of a function algebraically?

To find the range of a function algebraically, you can first solve for the function's output values by plugging in different input values and creating a table of values. Then, you can look at the output values and determine the set of all possible values, or the range.

## 3. Can the range of a function be infinite?

Yes, the range of a function can be infinite if the function has a horizontal asymptote or if the function is unbounded in either direction.

## 4. How can you visually determine the range of a function?

To visually determine the range of a function, you can plot the function on a graph and look at the y-values of the points on the graph. The range will be the set of all possible y-values that the function can produce.

## 5. Is the range of a function always a continuous set of values?

No, the range of a function does not always have to be a continuous set of values. It can also be a discrete set of values, such as a set of specific integers or fractions.

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