Question

Find the domain restriction. Fill in the table do preserved pairs, and graph the square root function. F(x)=squrt x-3

Table
X & Y
3
4
7
12

Answer 1

\(\Huge\color{blue}{ \bf ƒ }\)\(\LARGE\color{blue}{ \bf (x)=\sqrt{x-3} }\)

can you complete your table , at first, by simply plugging in the numbers you are given for domain ?

Answer 2

The domain can be all real numbers besides those that are less than 3, do you agree? Becuase if x<3 then f(x)="imaginary number " .

Answer 3

\(\LARGE\color{blue}{ \bf f(x)=\sqrt{x-3} }\)

if x=3, \(\LARGE\color{blue}{ \bf f(x)=\sqrt{3-3}=\sqrt{0} =0 }\)

if x=4, \(\LARGE\color{blue}{ \bf f(x)=\sqrt{4-3}=\sqrt{1} =±1 }\)

if x=7, \(\LARGE\color{blue}{ \bf f(x)=\sqrt{7-3}=\sqrt{4} =±2 }\)

if x=12, \(\LARGE\color{blue}{ \bf f(x)=\sqrt{12-3}=\sqrt{9} =±3 }\)

This are the ranges ( found by plugging in the domains into the function)