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MATHS 3^x graph

I don't understand why 3^x graph has a range of y>0 :frown: why isn't it y greater than equal to 0
Reply 1
Avatar for Notnek
Notnek
21
Original post by Jane122
I don't understand why 3^x graph has a range of y>0 :frown: why isn't it y greater than equal to 0

For what value of x do you think 3^x = 0 ?
Reply 2
Avatar for Jane122
Jane122
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2
Original post by notnek
For what value of x do you think 3^x = 0 ?


idk..
Reply 3
Avatar for JLegion
JLegion
2
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.
y approaches 0 as x tends to negative infinity, but doesn't equal 0.
(edited 7 years ago)
Reply 5
Avatar for Jane122
Jane122
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2
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
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.
Reply 7
Avatar for JLegion
JLegion
2
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.
Reply 8
Avatar for Jane122
Jane122
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2
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
Reply 9
Avatar for Naruke
Naruke
11
Original post by Jane122
I don't understand why 3^x graph has a range of y>0 :frown: 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, y=0 y = 0 would be the line the function gets infinitely close to!

95de3edc03c837b6c45493663485268d.png
Reply 10
Avatar for Jane122
Jane122
OP
2
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, y=0 y = 0 would be the line the function gets infinitely close to!

95de3edc03c837b6c45493663485268d.png

Are Solomon worksheets good
Reply 11
Avatar for Naruke
Naruke
11
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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