Question

Graph the function f(x)=1/2 sqrt(x+1)

Answer 1

The function is defined only if $x+1 \geq 0 \iff x \geq -1$. So, the leftmost point is $x=-1$, and we have

$f(-1)=\frac{1}{2}sqrt(-1+1) = 0$

So, the first point is $(-1,0)$

The three additional points seem arbitrary, so let's choose $x=0,1,2$. We have:

$f(0)=\frac{1}{2}sqrt(0+1) = \frac{1}{2}$

So, the second point is $(0,\frac{1}{2})$

$f(1)=\frac{1}{2}sqrt(1+1) = \frac{\sqrt{2}}{2}$

So, the third point is $(1,\frac{\sqrt{2}}{2})$

$f(2)=\frac{1}{2}sqrt(2+1) = \frac{\sqrt{3}}{2}$

So, the fourth point is $(2,\frac{\sqrt{3}}{2})$