Answer:
1) For \(y=5x\)
A) Domain= \((-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]\)
B) Range= \((-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]\)
C) y-intercept = 0
D) Asymptote= No asymptote
2) For \(y=log_5x\)
A) Domain=Domain= \((0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]\)
B) Range= \((-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]\)
C) y-intercept = None
D) Vertical Asymptote:
x=0
Step-by-step explanation:
Given : \(y=5x\) and \(y=log_5x\)
Refer the graph attached.
1) In equation (1) \(y=5x\)
→The domain is the set of all possible values in which function is defined.
y=5x is a linear polynomial defined on all real numbers.
Domain= \((-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]\)
→Range is the set of all values that function takes.
It also include all real numbers.
Range= \((-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]\)
→y-intercept- Value of y at the point where the line crosses the y axis.
put x=0 in equation y=5x we get, y=0
Therefore, y-intercept = 0 (We can see in the graph also)
→An asymptote is a line that a curve approaches, but never touches.
Asymptote= No asymptote
2) Now in equation (2) \(y=log_5x\)
Domain= \((0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]\)
because log function is not defined in negative.
Range= \((-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]\)
y-intercept - None
Vertical Asymptote:
x=0
