# How do you graph f(x)=sqrt(x-3)+4?

Feb 3, 2015

First of all I have to be careful with the square root. I do not want a negative argument, so I set:
$\left(x - 3\right) \ge 0$ and so:
$x \ge 3$
This means that I can only give values of $x$ starting from $3$ and going up (I cannot give $2$, $1$, $0$ etc..)

Then I'll choose "friendly" values of $x$ in the sense that using them I can easily evaluate the square root:

For example:
$x = 3$ $\to$ $y = 0 + 4 = 4$
$x = 4$ $\to$ $y = 1 + 4 = 5$
$x = 7$ $\to$ $y = 2 + 4 = 6$
$x = 12$ $\to$ $y = 3 + 4 = 7$
...etc

I can now plot my graph: