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Anika [276]
3 years ago
14

Graph f(x) = log1 X-3.

Mathematics
1 answer:
OlgaM077 [116]3 years ago
4 0

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 \:

<u><em>Determining x-intercept:</em></u>

\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)

<u><em /></u>

<u><em>Determining y-intercept:</em></u>

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.

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