Radical Functions: Graphing Radical Functions and Domain and Range

Graphing Square Root and Cube Root Functions

Now that you have gone through the values of "a", "b", "h", and "k", work through some examples.

Name the translations of the function f of x equals two times the square root of negative x plus three, minus one and graph the function.

The first thing that you should notice is that this isn't written exactly in y equals a times the square root of b times the quantity x minus h, plus k form. You need to factor the b out of the expression –x + 3.

-x + 3 = -1(x – 3)

Now you can rewrite this function as f of x equals two times the square root of negative one times the quantity x minus three, minus one.

You can now identify the translations:

a = 2
Vertical stretch by a factor of 2.

b = -1
Reflection across the y-axis.

h = 3
Horizontal translation of 3 units to the right.

k = -1
Vertical shift of 1 unit down.

You are ready to graph the function. The green graph is of the parent function f of x equals square root of x. The red graph is of your transformed function f of x equals two times the square root of negative one times the quantity x minus three minus one.

Green graph is f of x equal to square root of x, it starts at the point (0, 0) and goes through (1, 1), (4, 2) and (9, 3). 2. Red graph is f of x equal to two times the square root of negative the quantity x minus three minus one, it starts at the point (3, -1) and goes through (2, 1), (-1, 3) and (-6, 5)
Graph of f of x equals square root of x and f of x equals two times the square root of negative one times the quantity x minus three minus one