Which of the following are exponential functions?

Question

Which of the following are exponential functions?

A. f(x)=1x
B. f(x)=0.8x+1
C. f(x)=(3.14)3x
D. f(x)=(7/3)x
E. f(x)=42x
F. f(x)=−(2)x
G. f(x)=(−2)x
H. f(x)=x4

Answer 1

It's hard to tell from the way you've entered the options. I can only speculate that some of these are actually exponents. For example, I would guess that F is really -2^x, with the x as the exponent. 

 

That said, an exponential function is one with the variable (often x) in the actual exponent. However, the base (the lower number) must be a positive number, which I believe rules out A and G (if they are actually 1^x and (-2)^x.

 

Assuming the following, I've answered yes or no for exponential:

 

• A. 1^x  No, because the base is 1, which would make this function a straight line no different from y=1
• B. 0.8x+1 No, as written here, this is a straight line. However, both 0.8^x+1 and 0.8^x+1 are exponential functions. See the difference?
• C. (3.14)^3x Yes
• D. (7/3)^x would be yes, (7/3)x would be no
• E. 42x no
• F. -(2)^x yes
• G. (-2)^x no, this is a very weird relation, as the output alternates + and - for integers, and doesn't exist for non-integers.
• H. x⁴ no, despite the exponent in this function, it is NOT the variable, so is not an exponential function. The variable must be in the exponent to be an exponential function.

Hope this helps a bit!