This document provides examples of solving radical equations both algebraically and graphically. It shows setting a radical equation equal to zero and solving for the roots, which are also the x-intercepts when graphing the equation. It then provides mental math practice problems involving function transformations and compositions as well as a list of test review problems.

1. Solving Radical Equations
Ex. a) Determine the roots of √x + 5 - 3 = 0
b) Find the x-intercepts by graphing
The roots of a radical equation are the same as the
x-intercepts of the graph of the equation.

2. Ex. a) Determine the roots of √x + 2 - 4 = 0
b) Find the x-intercepts by graphing

3. and graphically.
√x + 5 = x + 3 algebraically

4. Mental Math
1. If (3, -2) is a point on the graph of f(x). What point must
be on the graph of y = 2f(x +1)?
2. Given f(x) = {(1, 3),(2, 5),(4, -1)}, state the domain of the
new function after f(x) is reflected through the line y = x.
3. What is the equation of f-1(x) if f(x) = 2x - 6?
4. Which transformation occurs first in y = -2|x| +1 ?
5. Where will the graph of √x have invariant points?

5. Test Review
p.255 #1-3, 5, 7, 9-11
p.146 #1 and worksheet