f(x)=sqrt x+3

Question

Graph the function. Graph the leftmost point and three additional points.

Answer 1

In the real number set, you can't take the square root of a negative number.  Therefore, the expression under the radical (known as the radicand) must be greater than or equal to zero:

 

     x+3 ≥ 0

 

or

 

      x ≥ -3

 

When you plug x = -3 into f(x), you get:

 

     f(-3) = √(-3+3) = √0 = 0.  The "leftmost point" then is (-3,0)

 

Now you need to plot 3 more points.  let's choose x = 1, x=6, and x = 13:

 

      x              f(x)      

     1       √(1+3) = 2

     6       √(6+3) = 3

    13      √(13+3) = 4

 

Plot the points (-3,0), (1,2), (6,3), (13,4) then connect the points with a smooth curve and continue past the last point.