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!

Expert Answers
durbanville eNotes educator| Certified Educator

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.


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



rakesh05 eNotes educator| Certified Educator

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.

alejandrogalarce | Student

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`

` `

aruv | Student


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


If a=0 then

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


intercept is (1/4)


We unable to plot graph.