QQuestionMathematics
QuestionMathematics
1. Which of the following are exponential functions?
\begin{aligned}
& \square f(x)= 10^{4 + 3 x} \\
& \text { - } f(x)=(- 5)^{x} \\
& \square f(x)=\left(\frac{1}{x}\right)^{6} \\
& \text { - } f(x)=\left(\frac{1}{4}\right)^{- 2 x}
\end{aligned}
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Identify the general form of an exponential function.
An exponential function is a mathematical function of the form f(2$) = abx, where a and b are constants, with b > 0 and b ≠ 1.
Step 2:: Analyze the first function.
f(x) = 10^{4+3x}
In this function, the base (10) is a constant, and the exponent is 4 + 3x. Since the exponent is a linear function of x, this is an exponential function.
Step 3:: Analyze the second function.
f(x) = (-5)^{x}
In this function, the base is (- 5), which is a constant. The exponent is x, which varies with the input. Since the base is a constant, this is an exponential function.
Step 4:: Analyze the third function.
f(x) = \left(\frac{1}{x}\right)^{6}
In this function, the base is (1 /x), which is not a constant since it depends on the input x. Therefore, this is not an exponential function.
Step 5:: Analyze the fourth function.
f(x) = \left(\frac{1}{4}\right)^{-2x}
In this function, the base is (1 / 4), which is a constant. The exponent is - 2x, which varies with the input. Since the base is a constant, this is an exponential function.
Final Answer
- f(2$) = 10^(4 + 3x) - f(2$) = (- 5)^x - f(2$) = (1 / 4)^(- 2x)
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students