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# MATHS 3^x graph

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1. I don't understand why 3^x graph has a range of y>0 why isn't it y greater than equal to 0
2. (Original post by Jane122)
I don't understand why 3^x graph has a range of y>0 why isn't it y greater than equal to 0
For what value of x do you think 3^x = 0 ?
3. (Original post by notnek)
For what value of x do you think 3^x = 0 ?
idk..
4. There is no value of x that makes y = 0
If y = 3^x, When:
x= 1, y = 3
x= 0, y= 1
x= -1 y = 1/3
x= -2, y = 1/9

This goes on forever, but will never reach y = 0 - only getting closer and closer to 0 but never actually reaching it.
5. y approaches 0 as x tends to negative infinity, but doesn't equal 0.
6. (Original post by JLegion)
There is no value of x that makes y = 0
If y = 3^x, When:
x= 1, y = 3
x= 0, y= 1
x= -1 y = 1/3
x= -2, y = 1/9

This goes on forever, but will never reach y = 0 - only getting closer and closer to 0 but never actually reaching it.
Is it because of the asymptote thing
7. Think about it this way.

If y=3^x, since y>0 it means that whatever real number you choose x to be, y>0.
Try with x=-1 ; y=3^(-1) = 1/3 > 0
Try with x= 0 ; y=3^0 = 1
Try with x=infinity ; y=3^(infinity) = infinity
Try with x=-infinity ; y=3^(-infty) = 1/infty = 0

Strictly though, we should use limits when talking about infinity but the above expanation works.

In other words, for all real values of x, y will always be greater than zero.
8. (Original post by Jane122)
Is it because of the asymptote thing
There is an asymptote at y = 0. y gets closer and closer to y = 0 but never actually touches it.
9. (Original post by JLegion)
There is an asymptote at y = 0. y gets closer and closer to y = 0 but never actually touches it.
Ok so it's cause of the asymptote
10. (Original post by Jane122)
I don't understand why 3^x graph has a range of y>0 why isn't it y greater than equal to 0
The range is defined as all the values the function outputs.

An asymptote is the vertical or horizontal line a function gets extremely close to, but never crosses it.

In this case, would be the line the function gets infinitely close to!

11. (Original post by Naruke)
The range is defined as all the values the function outputs.

An asymptote is the vertical or horizontal line a function gets extremely close to, but never crosses it.

In this case, would be the line the function gets infinitely close to!

Are Solomon worksheets good
12. (Original post by Jane122)
Are Solomon worksheets good
Yeah, but work on them once you've competed the textbook questions.

Good luck fam

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