Question

identify the domain, range, intercept, and asymptote of the exponential function. then describe the end behavior

f(x)=5·7^x

e all real numbers

find the range of the function f(x)=5·7^x. choose the correct answer below and, if necessary, fill in the answer box to complete your choice

a {y|y>}
b {y|y=}
(use a comma to separate answers as needed.)

c {y|y<}

d {y|y≠}
(use a comma to separate answers as needed.)

e all real numbers

Explanation:

Step1: Analyze the exponential function \(y = a\cdot b^{x}\) form

For the function \(f(x)=5\cdot7^{x}\), where \(a = 5>0\) and \(b = 7>1\). The general form of an exponential function is \(y=a\cdot b^{x}\). When \(a>0\) and \(b > 1\), the range of \(y=a\cdot b^{x}\) is based on the fact that \(b^{x}>0\) for all real \(x\).

Step2: Find the range

Since \(7^{x}>0\) for all \(x\in R\), and \(y = 5\cdot7^{x}\), then \(y>0\) (multiplying a positive number \(5\) with a positive number \(7^{x}\)).

Answer:

A. \(\{y|y > 0\}\)