Question

How do you graph `y= 9(3)^(2x)` using a table of values?

Answer 1

`" "`
Please read the explanation.

Explanation:

`" "`
The function given

`color(red)(y=f(x)=(9)(3)^(2x)`

is an exponential function.

The parent function of the exponential function `color(blue)(y=a*b^x` has

base `color(red)(b` with exponent `color(red)(x`

y-intercept: `color(red)((0,a)`

Conditions:

`color(green)(b>0`

`color(green)(b!=1`

Values of `color(red)(x` are extremely small in the second quadrant close to the x-axis, but in the first quadrant you can observe the values of `color(red)(y` increase rapidly.

Data table is given below:

Graph of `color(red)(y=f(x)=(9)(3)^(2x)`:

You can also find the graphs of `y=3^(2x)` and `y=2^x` for comparison.

Hope it helps.