Question

What are the `x`-intercept and `y`-intercept of `y=-(2)^x+8`?

Answer 1

`x = 3 and y = 9`

Explanation:

At the `y` intercept, we know that `x = 0`. By substituting that into the equation we get;

`y = -2^0 + 8`
`y = 1+8`
`y=9`

At the `x` intercept, we know that `y = 0`. By substituting that into the equation we get;

`0 = -2^x + 8`
`8 = 2^x`

`x = 3`

Answer 2

`"The X-intercept is "3", and, the Y-intercept is "9`.

Explanation:

The `X`-intercept and the `Y`-intercept of a curve `C : y=f(x)` are

the `X`-co-ord. (i.e., Abscissa ) and the `Y` co-ord.

(i.e., Ordinate ) s. of the pt. of intersection of `C` with `X`-axis

(eqn., `y=0`) and `Y`-axis (eqn., `x=0`), resp.

So, to get them, we have to solve the resp. eqns.

Accordingly, for the `X`-intercept, we have to solve the eqns. :

`y=-2^x+8, and, y=0 rArr 2^x=8=2^3 rArr x=3.`

Therefore, the `X`-intercept of `C" is "3`

Similarly, the `Y`-intercept of `C" is "9.`,