Which functions in the table below give values that could come from exponential functions? Check all that apply.

a. f(x)
b. g(x)
c. h(x)
d. k(x)

Question

Which functions in the table below give values that could come from exponential functions? Check all that apply.

         a. f(x) 
         b. g(x) 
         c. h(x) 
         d. k(x)

anonymous · Answer

attachment

anonymous · Answer

i think its g(x)=2^x

mathstudent55 · Answer

An exponential function is of the form 

$ f(x) = k^x$

where k is a positive real number, $k \ne 1$.

mathstudent55 · Answer

Look at f(x)
The values of f(x) are 1, 4, 9, 16, 25, 36, 49
What do those values remind you of?

anonymous · Answer

so an exponential function can't be a decimal?

mathstudent55 · Answer

A function is not a number.
An exponential function can be:

$f(x) = 4^x$

$g(x) = e^x$

$h(x) = (\dfrac{1}{2})^x$

These are all examples of exponential functions.

Notice that in every case, you have a positive number that is real and not equal to one raised to x.

anonymous · Answer

so the only answer that works is f(x)?

mathstudent55 · Answer

I didn't say that. I asked you a question about f(x), but you never answered.
Do the numbers 1, 4, 9, 16, 25, 36, 49 remind you of something?

anonymous · Answer

umm no

mathstudent55 · Answer

Try the squares of whole numbers.

anonymous · Answer

I don't understand. I'm sorry.

mathstudent55 · Answer

$1^2 = 1$
$2^2 = 4$
$3^2 = 9$
$4^2 = 16$
$5^2 = 25$
$6^2 = 36$
$7^2 = 49$

anonymous · Answer

oh I see!

mathstudent55 · Answer

Every exponent is 2. What chanbes is the base. In an exponential function, the base is always the same, and the exponent changes. That means f(x) is not an exponential function.

mathstudent55 · Answer

In other words, $f(x) $ in your problem is related to $f(x) = x^2$.
This is not an exponential function.
An exponential function has x in the exponent, not in the base.

anonymous · Answer

oh okay

anonymous · Answer

I'm really confused on how to do the ones with decimals...

mathstudent55 · Answer

Ok, let's look at the second one.
Start with x = 0 through x = 3
An exponential function has a number raised to the x power.
What number can you raise tot eh second power and get 4?
The same number raised to the 3rd power equals 8?

mathstudent55 · Answer

$g(x) = k^x$

$g(0) = k^0 = 1$
$g(1) = k^1 = 2$
$g(2) = k^2 = 4$
$g(3) = k^3 = 8$

What number can you put in for k above to make the equations true?

mathstudent55 · Answer

Look at $g(1) = k^2 = 2$. What number raised to the 1 power equals 2?

anonymous · Answer

2

mathstudent55 · Answer

Correct. That means that the second choice, $g(x) = 2^x$
$g(x)$ is an exponential function.

mathstudent55 · Answer

Now let's look at the third choice, h(x).
Notice that for every increases in x of 1, h(x) increases 0.25.
That makes it a linear equation, which is certainly not an exponential function.

mathstudent55 · Answer

Finally we get to k(x).
Remember that in an exponential function, you have a non-1 positive number raised to the x power.
When you raise a positive number to the zero power, what do you get?
For example, what are $3^0$, $5^0$, $1.5^0$ equal to?

mathstudent55 · Answer

Now look at what k(0) equal to?

anonymous · Answer

1

anonymous · Answer

is it 1?

mathstudent55 · Answer

No. Look in the table.
For x = 0, k(x) = k(0) = 0
An exponential function has to be a positive number raised to x.
Any positive number raised to 0 equals 1.
Since k(0) = 0, not 1, that means k(x) can't be an exponential function.

mathstudent55 · Answer

That means the only exponential function is choice B. g(x).