Which best describes the graph of the function f(x) = 4(1.5)x? The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by 1.5. The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5. The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by 4. The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by a factor of 4.

The correct option is:

The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5.

Step-by-step explanation:

The function given to us is:

f(x) = 4(1.5)ˣ

Substitute x = 0 in the given function:

f(0) = 4(1.5)⁰

f(0) = 4(1)

f(0) = 4

Which means that the graph pass through the point (0,4)

Now Substitute x = 1 in the given function:

f(1) = 4(1.5)¹

f(1) = 6

Substitute x =2 in the given function:

f(2) = 4(1.5)²

f(2) = 9

Divide the consecutive values:

f(2) / f(1) = 9/6 = 1.5

f(1) / f(0) = 6/4 = 1.5

Hence the values of y increase by the factor of 1.5