Question

What is the domain of f(x) = 5x – 7?

{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}

I think it is {x | x > –7}

Answer 1

Or simply a site to figure out the range and domain of exponential functions...

Answer 2

When finding the domain, you really just have to think about what x-values you can NOT plug into a function. But that seems to be a pretty difficult thing for most students to grasp.

This might help http://www.coolmath.com/algebra/15-functions/06-finding-the-domain-01

Answer 3

f(x) = 5x – 7 is the equation of a line, not an exponential function.

Answer 4

I still do not understand...

Answer 5

Did you read any of the link I posted?

Answer 6

The domain is the set of all acceptable values of x.

Is there any value of x that you see that should be excluded? @pianochica

Answer 7

I read it all. It just confused me more. How do I know what numbers to plug in? Do I always plug in zero?

Answer 8

You posted this as the answer: I think it is {x | x > –7}

That means that a value of x such as -10 is excluded from the domain.

Yet, if x = -10, f(-10) = 5* (-10) – 7 = -57

Answer 9

You have to just try to think about whether there are any numbers you can NOT plug in to a function.

Like if y = 1/x, you should know that you can't divide by zero, so x=0 is NOT in the domain. Every other value of x is fine.

Answer 10

So, why would you exclude -10 from the domain? @pianochica

Answer 11

I... do not understand any of this... I don't understand what I am even supposed to be looking for to be able to solve it. How do I know what numbers won't fit?

Answer 12

Domain isn't an easy concept to grasp.

Any number that won't fit, would be one the gives you a result that doesn't make sense.

Like if you plug in a number, and as a result will be dividing by zero.

Or if you plug in a number, and as a result you get the square root of a negative number.

Answer 13

Look at f(x) = 5x – 7.

There's no square root of x, right?

There's also no x in a denominator of a fraction.

Answer 14

No square root and no x in a denominator of a fraction... But how does that help?

Answer 15

See the last two statements in my previous post as to why that helps.

Answer 16

In this equation, is there any number you can plug in, that would lead to dividing by zero, or the square root of a negative?

Answer 17

No, so would it be any real number? I've tried plugging in -9 and 6 and they made sense... But i plugged in 0 and ended up with 0-7 which ultimately is -7. Is there a rule domains have to be positive numbers?

Answer 18

The *result* that you get after plugging in a number is not the domain, the result is part of the range.

The number you plug in is in the domain.

As long as the result is a real number (ie not the square root of a negative, or something where you're dividing by zero), then that value you plugged in is fine.

And that's a good way to find out - test positive and negative values of x, see if the results make sense.

Answer 19

So how do I figure out the range? What exactly is range? I really do not understand any of this...

Answer 20

This question is about the domain, not the range.

The domain is the values you plug in (those are x values). The range is the y values.

The domain are the values you plug in (the input values)

Range is the output values.

Answer 21

What is the domain of f(x) = 3x – 2?

{x | x > 0}
{x | x < 0}
{x | x = 0}
{x | x is a real number}

SO in this problem, it would be x is a real number because -5, 5, and 0 all make sense with the equation?

Answer 22

Well it's not just a real number because -5, 5, and 0 all make sense in the equation. It's real numbers because ANY value you plug in will make sense. But checking -5, 5 and 0 is a good start.

Answer 23

Okay, thank you. I think I am beginning to understand it now. So even if I plugged in say, 1.54 it'd still work?

Answer 24

Don't ask me, check for yourself :)

Answer 25

Thank you for your help! I think I understand it now! :)

Answer 26

You're welcome.

Keep in mind that plugging in numbers won't always work, if you just happen to plug in some numbers that work - that doesn't mean ALL real numbers will work.

Basically you just need to look out for x's inside square roots, and x's in denominators.