Given the function:
[tex]f(x)=\sqrt[]{x+4}[/tex]
This function is a radical function. The domain of this function comprehends any value of x for which the radicand is not negative.
The leftmost point of the function is determined by the value of x for which the radicand is zero.
To determine this value of x, you have to equal the radicand to zero and solve:
[tex]\begin{gathered} x+4=0 \\ x+4-4=0-4 \\ x=-4 \end{gathered}[/tex]
For x=-4 the radicand is equal to zero and the function is also equal to zero, so the coordinates for the leftmost point are:
[tex](-4,0)[/tex]
For the next three points, you have to choose 3 positive values of x, replace them into the formula and solve for f(x).
I will use 0, 5, and 12
For x=0
[tex]\begin{gathered} f(x)=\sqrt[]{x+4} \\ f(0)=\sqrt[]{0+4} \\ f(0)=\sqrt[]{4} \\ f(0)=2 \end{gathered}[/tex]
The coordinates are:
[tex](0,2)[/tex]
For x= 5
[tex]\begin{gathered} f(x)=\sqrt[]{x+4} \\ f(5)=\sqrt[]{5+4} \\ f(5)=\sqrt[]{9} \\ f(5)=3 \end{gathered}[/tex]
The coordinates are:
[tex](5,3)[/tex]
For x= 12
[tex]\begin{gathered} f(x)=\sqrt[]{x+4} \\ f(12)=\sqrt[]{12+4} \\ f(12)=\sqrt[]{16} \\ f(12)=4 \end{gathered}[/tex]
The coordinates are
[tex](12,4)[/tex]
Once you have determined the coordinates of the four points, plot them and graph the function:
