1. Solve the radical equation
Warm Up
Solve the radical equation
Use the description to write the quadratic function g based on the parent function f(x) = x2.
f is translated 3 units up.
f is translated 2 units left.

2. HW Check
Solve the following Radical Equations

3. What do you remember about the parent function of:
What about the domain and range?

4. Recall that exponential and logarithmic functions are inverse functions. Quadratic and cubic functions have inverses as well. The graphs below show the inverses of the quadratic parent function and cubic parent function.

5. Notice that the inverses of f(x) = x2 is not a function because it fails the vertical line test. However, if we limit the domain of f(x) = x2 to x ≥ 0, its inverse is the function
A radical function is a function whose rule is a radical expression. A square-root function is a radical function involving . The square-root parent function is The cube-root parent function is

6. Transformations of square-root functions are summarized below.

7. Describe the Transformation and the Domain and Range

8. Example 2: Transforming Square-Root Functions
Using the graph of as a guide, describe the transformation and graph the function. Also describe the domain and range
f(x) = x
g(x) = x + 5

9. Check It Out! Example 2a
Using the graph of as a guide, describe the transformation and graph the function. Also state the domain and range
f(x)= x
g(x) = x+1

10. Check It Out! Example 2b
Using the graph of as a guide, describe the transformation and graph the function. Also state the domain and range
f(x) = x

11. Example 3: Applying Multiple Transformations
Using the graph of as a guide, describe the transformation and graph the function Also state the domain and Range
f(x)= x .

12. Check It Out! Example 3a
Using the graph of as a guide, describe the transformation and graph the function. Also state the domain and Range.
f(x)= x

13. Check It Out! Example 3b
Using the graph of as a guide, describe the transformation and graph the function. Also state the domain and Range
f(x)= x
g(x) = –3 x – 1