Question

Which of the following functions shown in the table attached could be an exponential function? List all of the answers that apply.

A. k(x)
B. h(x)
C. f(x)
D. g(x)

Answer 1

i believe is C

Answer 2

Take the last function in the table, k(x), for example. You can see the each x value is a fourth of the previous x value. We can guess the equation is:
k(x) = (1/4)^x
You can trying putting x = -3, -1, 0, 1, etc.
So k(x) is an exponential function because a general exponential function is of the form:
y = A*(B)^x

Try to see similar patterns in h(x), g(x), etc and see if you can guess the equation.

Answer 3

I'm thinking g(x) is also an exponential function, is that correct?

Answer 4

Because each time it increases by .25

Answer 5

I will tell you another method:

The general exponential function is y = A * (B)^x
Take two data points from the table, put it into y = A * (B)^x and solve for A and B.
Choose the data points with x = 0 and x = 1.
See if the rest of the data obeys the equation. If it does then it is an exponential function. If it does not then it is not.

I will do one example.
Assume k(x) = A * (B)^x ----- equation (1)
From the table, x = 0, k = 1
1 = A * B^0 = A. So A = 1. Thus, equation (1) becomes k(x) = B^x
From the table x = 1, k = 0.25 or 1/4
1/4 = B^1. Thus, B = 1/4
k(x) = (1/4)^x

Try other values of x in the equation k(x) = (1/4)^x.
x = -2, k(x) = (1/4)^(-2) = 4^2 = 16
This value agrees with the table and therefore k(x) is an exponential function.

Try the same with other functions.

Answer 6

so h(x) wouldn't be an exponential function even though it increases by .25 because it increases through addition and not multiplication?

Answer 7

Exactly! h(x) is NOT an exponential function because it increases through addition and not multiplication.
h(x) just increases by a 1/4 every time. It goes 1/4, 1/2, 3/4, 1, 1&1/4, etc.
It is a linear function. It is a straight line. You can even find the equation of that straight line: h(x) = 1/4x + 1. So h(x) is NOT an exponential function.

Answer 8

Oh I see! Let me test out the otheres really quick!

Answer 9

And yes, g(x) is also an exponential function because we are multiplying by 2 everytime.

Answer 10

I dont think that f(x) is an exponential function because it increases by a different number each time..

Answer 11

Yes. Of all the three functions, the f(x) is the only one I will try to find the equation by solving for A and B as shown above. And you will find it is not an exponential function.

Answer 12

So only k(x) and g(x) are exponential functions correct?

Answer 13

If we cannot fit a y = A * B^x into the data then it is not an exponential function.

Yes, only k(x) and g(x) are exponential functions.

Answer 14

thank you so much for explaining this to me!! :)

Answer 15

you are welcome.