Question

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

to do so, graph the lefmost point and three additional points.
What are the 4 graph points?

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)=(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)=(1)/(2)sqrt(0+1) = (1)/(2)`

So, the second point is
`(0,(1)/(2))`

`f(1)=(1)/(2)sqrt(1+1) = (√(2))/(2)`

So, the third point is
`(1,(√(2))/(2))`

`f(2)=(1)/(2)sqrt(2+1) = (√(3))/(2)`

So, the fourth point is
`(2,(√(3))/(2))`