for the function f(x)=(1/2) - 6^x, identify the domain, range, y - intercept, and asymptote. write one of…

Explanation:

Step1: Find domain

For exponential functions like $f(x)=\frac{1}{2}\cdot6^{x}$, there are no restrictions on $x$. So the domain is all real numbers.

Step2: Find range

Since $6^{x}>0$ for all real - valued $x$, and $f(x)=\frac{1}{2}\cdot6^{x}$, then $f(x)>0$. So the range is ${y|y > 0}$.

Step3: Find y - intercept

To find the y - intercept, set $x = 0$. Then $f(0)=\frac{1}{2}\cdot6^{0}=\frac{1}{2}\times1 = 0.5$.

Step4: Find asymptote

As $x\to-\infty$, $6^{x}\to0$. So $y = 0$ is the horizontal asymptote of the function $f(x)=\frac{1}{2}\cdot6^{x}$.

Answer:

Domain: all real numbers Range: ${y|y > 0}$ Function type: exponential y - Intercept: $0.5$ Asymptote $y = 0$