MATHS 3^x graph

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Jane122
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#1
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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
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Notnek
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#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 ?
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Jane122
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(Original post by notnek)
For what value of x do you think 3^x = 0 ?
idk..
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JLegion
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#4
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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.
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NotNotBatman
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#5
y approaches 0 as x tends to negative infinity, but doesn't equal 0.
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Jane122
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#6
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(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
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aerofanatic
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#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.
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JLegion
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(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.
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Jane122
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#9
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#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
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Naruke
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#10
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#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,  y = 0 would be the line the function gets infinitely close to!

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Jane122
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(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 would be the line the function gets infinitely close to!

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Are Solomon worksheets good
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Naruke
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#12
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#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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