Math

QuestionIdentify the exponential parent function from the options: A. f(x)=xf(x)=x, B. f(x)=2xf(x)=2^{x}, C. f(x)=xf(x)=|x|, D. f(x)=x2f(x)=x^{2}.

Studdy Solution

STEP 1

Assumptions1. The exponential parent function is in the form of f(x)=axf(x) = a^{x}, where aa is a constant and a>0a >0. . f(x)=xf(x) = x is a linear function.
3. f(x)=xf(x) = |x| is an absolute value function.
4. f(x)=xf(x) = x^{} is a quadratic function.

STEP 2

Now, we compare each of the given functions with the form of the exponential parent function.

STEP 3

First, we look at option A. f(x)=xf(x) = x.
This function is not in the form of f(x)=axf(x) = a^{x}, so it is not an exponential parent function.

STEP 4

Next, we look at option B. f(x)=2xf(x) =2^{x}.
This function is in the form of f(x)=axf(x) = a^{x}, where a=2a =2. So, it is an exponential parent function.

STEP 5

Then, we look at option C. f(x)=xf(x) = |x|.
This function is not in the form of f(x)=axf(x) = a^{x}, so it is not an exponential parent function.

STEP 6

Finally, we look at option D. f(x)=x2f(x) = x^{2}.
This function is not in the form of f(x)=axf(x) = a^{x}, so it is not an exponential parent function.

STEP 7

After comparing all the options, we find that only option B. f(x)=2xf(x) =2^{x} is an exponential parent function.
So, the solution to the problem is option B. f(x)=2xf(x) =2^{x}.

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