Question

Sketch the graph of the given data on the accompanying coordinate plane. a)choose ad state an appropriate scale so that all of the points can be plotted. b) write a function rule for the data.
X= 0 1 2 3 4
F(x)= 1 3 9 27 81

Answer 1

Part A
A good scale for y to use would be 100, since it fits in all of the f(x)'s and the next value (243) is obviously not going to fit.
As for x, you can use 4 or 5. If you do 5, you're not going to get to it though, because f(x) will be 243.

Part B
When our input increases by 1, our output multiplies by 3.
Multiplying by 3 $x$ times can be represented as $3^x$.
We start at 1, so we'd want to have $1\times3^x$. However, 1 times anything doesn't change its value, so we can leave it out because it is redundant.

As for making the graph, just label your y axis 0 to 100, and your x axis 0 to 5.
Then mark out (0, 1), (1, 3), (2, 9), (3, 27), and (4, 81).
Draw a curve that includes all of these. It should hit y=100 a little after x=4, since x=5 is all the way at y=243.