which of the following is not an exponential function?\n$f(x)=5^{x}$\n$g(x)=(\\frac{4}{7})^{x}$\n$h(x)=(\\sqr…
which of the following is not an exponential function?\n$f(x)=5^{x}$\n$g(x)=(\\frac{4}{7})^{x}$\n$h(x)=(\\sqrt{3})^{x}$\n$k(x)=x^{2}$
Answer
Explanation:
Step1: Recall the form of an exponential function
An exponential function is of the form (y = a^{x}), where (a>0), (a\neq1), and (x) is the independent variable.
Step2: Analyze each function
- For (f(x)=5^{x}), here (a = 5>0) and (a\neq1), so it is an exponential function.
- For (g(x)=\left(\frac{4}{7}\right)^{x}), here (a=\frac{4}{7}>0) and (a\neq1), so it is an exponential function.
- For (h(x)=(\sqrt{3})^{x}), here (a = \sqrt{3}>0) and (a\neq1), so it is an exponential function.
- For (k(x)=x^{2}), it is a quadratic function (of the form (y = x^{n}) where (n = 2) is a constant, not an exponential function of the form (y=a^{x})).
Answer:
(k(x)=x^{2}) (the fourth option) is not an exponential function.