Question

Which graph best represents the function f(x) = 1(1.5)x?

Answer 1

That would be the third graph
when x = 0, 1(1.5)^0 = 1*1 = 1
when x = 1 , its equals 1.5

both these points are only on this graph

Answer 2

The third graph with y-interception at (0,1) represents the given exponential function.

Explanation:

The given function is

`f(x)=1(1.5)^(x)`

This function can be seen as a parent function, that is, a simple exponential function. The important thing about it is that parent exponential functions has the y-interception at (0,1), because for x = 0, always y = 1.

We can demonstrate that by replacing x = 0

`f(x)=1(1.5)^(x)\\f(0)=1(1.5)^(0)=1(1)=1`

This means that the graph that represents
`f(x)` has the y-interception at (0,1).

As you can observe, the third graph is the one that has this characteristic. Because the first graph intercepts at (0,2), the second graph at (0,3) and the fourth graph at (0,4).

Therefore, the right answer is the third graph with y-interception at (0,1).