Question

Graph f(x) = log1 X-3.

Answer 1

Answer:

The graph of the function  $f\left(x\right)=\:\log _{10}\:x-3$  is attached below.

Step-by-step explanation:

Considering the function

$f\left(x\right)=\:\log _{10}\:x-3$

$\mathrm{Domain\:of\:}\:\log _{10}\left(x\right)-3\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Range\:of\:}\log _{10}\left(x\right)-3:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

Determining x-intercept:

$\mathrm{x-intercept\:is\:a\:point\:on\:the\:graph\:where\:}y=0$

$\log _{10}\left(x\right)-3=0$

$\log _{10}\left(x\right)=3$

Using the logarithmic definition

$\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c$

$\log _{10}\left(x\right)=3\quad \Rightarrow \quad \:x=10^3$

$x=1000$

so the x-intercept = (1000, 0)

Determining y-intercept:

$y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0$

$\mathrm{Since}\:x=0\:\mathrm{is\:not\:in\:domain}$

$\mathrm{No\:y-axis\:interception\:point}$

Therefore, the graph of the function  $f\left(x\right)=\:\log _{10}\:x-3$  is attached below.