Need help solving this one

Question

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

f(x)=(sqrt x)+4

Answer 1

Graphing square root functions has to do with manipulating the parent, or simplest form of, the function. The simplest form of this function is f(x)=(sqrt x). This graph begins at the point (0,0) and continues right and up, including the points (1,1), (4, 2), and (3,9).

Other equations are all manipulations of the parent function. We can call a general function f(x) = a(sqrt (x - h)) + k.

a will tell you about the vertical scaling of the graph. If the absolute value of a is greater than 1, this function will grow vertically a times more quickly than the parent function. If the absolute value of a is greater than 0 but less than 1, this function will grow a times more slowly than the parent function. If a is negative, this function and its scaling will be flipped over the x-axis.

h tells you about the horizontal shift. If you're subtracting h from x, you're moving the parent function h spots to the right. If you're adding h to x, you're moving the parent function h spots to the left.

k tells you about the vertical shift. If you're adding k, you're moving the parent function up k spots. If you're subtracting k, you're moving the parent function down k spots.

Finally, the coordinate (-h, k), where you use the operation in front of h to determine if it is positive or negative, will give you the starting point of your graph.

Whew, that was a lot! In your particular problem, there isn't any vertical scaling (no a value), nor do we have horizontal shift (no h value). We do have a positive vertical shift (k value) that will move the parent function 4 spots up. So, we add 4 to the y value of the coordinates for the parent function to find the coordinates for this new function.

Parent function: (0, 0) (1, 1) (4, 2) (9, 3)

New function: (0, 4) (1, 5) (4, 6) (9, 7)

I hope this helps!