which of these is an exponential parent function?\na. (f(x)=2^{x}+\frac{2}{3})\nb. (f(x)=2^{x})\nc…

which of these is an exponential parent function?\na. (f(x)=2^{x}+\frac{2}{3})\nb. (f(x)=2^{x})\nc. (f(x)=2^{x}-3)\nd. (f(x)=2^{x}+2)

which of these is an exponential parent function?\na. (f(x)=2^{x}+\frac{2}{3})\nb. (f(x)=2^{x})\nc. (f(x)=2^{x}-3)\nd. (f(x)=2^{x}+2)

Answer

Explanation:

Step1: Recall parent - function definition

An exponential parent function has the form $f(x)=a^x$ where $a>0,a\neq1$ and there are no vertical or horizontal shifts, and no vertical stretches or compressions other than the base - value $a$.

Step2: Analyze each option

  • Option A: $f(x)=2^x+\frac{2}{3}$ has a vertical shift of $\frac{2}{3}$ units up, so it is not a parent function.
  • Option B: $f(x)=2^x$ is in the form $f(x)=a^x$ with $a = 2>0,a\neq1$ and no shifts or additional operations, so it is an exponential parent function.
  • Option C: $f(x)=2^x - 3$ has a vertical shift of 3 units down, so it is not a parent function.
  • Option D: $f(x)=2^x+2$ has a vertical shift of 2 units up, so it is not a parent function.

Answer:

B. $f(x)=2^x$