Question

I need to double check if I got the right answer. I chose C.

Answer 1

It is required to choose the graph that correctly represents the function:

`f(x)=3\left((1)/(2)\right)^x`

Recall that an exponential function is of the form:

`f(x)=a(b)^x`

With b greater than 0, but not equal to 1.

Recall also that if b<1, then the exponential function is a decreasing function.

Hence, the possible graphs are C or D.

Calculate the y-intercept by substituting x=0 into the equation, and then compare with the graphs C or D:

`f(0)=3\left((1)/(2)\right)^0=3\cdot1=3`

It follows that the y-intercept is 3.

Notice that only graph C has a y-intercept of 3 between C and D.

Hence, the correct graph is graph C.

The correct graph is graph C.