Question

The graph of an exponential function of the form y=f(x)=a^x passes through the points 1. ____ and 2. ____ . The graph lies 3. ____ the x-axis?

1. (0.a), (0,1), (0,2), (0,-1)
2. (1,0), (1,1), (1,a), (1,-2)
   3.(above), (below), (on the)

Answer 1

(0,1) (1,a) above

Explanation:

when `x` is `0`, `a^x` is `a^0`.

any number to the power of `0` is `1`, so `a^0` must be `1`.

`f(x)` (or `y`) is `a^x`, so when `x = 0`, `y = 1`. this gives coordinates `(0,1)`.

any number to the power of `1` is the number itself, so `a^1` is always `a`.

when `x = 1`, `f(x) = a^1 = a`
`x = 1, y = a`, giving coordinates `(1,a)`.

assuming that `a` is positive, `a` cannot be raised to a power to become a negative number.

(negative powers give reciprocals of positive powers, and fractional powers give positive roots.)

this means that all the `y`-coordinates of the graph will be above `0`.

on the `x`-axis, all `y`-coordinates are `0`. this means that all points on the graph will be above (with a higher `y`-coordinate than) the `x`-axis.