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1. What is the y-intercept of the graph of `y=a^(x-2)`  y-intercept: answer is...

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alejandrogalarce | Student, Undergraduate | Valedictorian

Posted June 3, 2013 at 6:41 AM via web

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1. What is the y-intercept of the graph of `y=a^(x-2)` 

y-intercept: answer is `a^(-1)`

 Please tell me how to get there!

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted June 3, 2013 at 7:15 AM (Answer #1)

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To solve an exponential graph, substitute the values such that if x= 0 (which indicates the y-intercept):

`y=a^(x-2)`  becomes : `y=a^(0-2)`

`therefore y=a^-2` Therefore(x;y): `(0;a^-2)`  

However this is not the answer required in terms of the question.

In order to get an answer of `y=a^-1` we need to substitute x=1:

`therefore y= a^(1-2)` Therefore (x;y): `(1;a^-1)`

This is NOT the y intercept as x=0 at that point.

Ans:

`(0; a^-2)` when x=0 or `(1;a^-1)` when y=`a^-1`

 

 

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aruv | High School Teacher | Valedictorian

Posted June 3, 2013 at 7:16 AM (Answer #2)

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`y=a^(x-2)`

y-intercept of this graph depends on a.

If `a>0`

substitute x=0 in given equation

`y=a^(0-2)=1/a^2`  is y intercept.

`if a<0`

substitute x=0 in given equation

`y=(-a)^(0-2)=1/a^2`

If a=0 then

`y=0^(x-2)=0AAx `  except x=2 because  `y=0^0`  is indeterminant form.

     `y=2^(x-2)`

intercept is (1/4)

`y=(-2)^(x-2)`

We unable to plot graph.

 

 

 

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alejandrogalarce | Student, Undergraduate | Valedictorian

Posted June 3, 2013 at 5:12 PM (Answer #3)

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For the graph of `y=a^(x-2)` , we can find the y-intercepts by substituting x=0. That is

`y=a^(0-2) =a^(-2)=1/a^2`

` `

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted June 5, 2013 at 7:21 AM (Answer #4)

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Actually when a<0 and x takes fractional values the fuction will not remain in R. So we can not take a<0 for all real values of x.

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