Solve the radical equation

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Presentation transcript:

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.

HW Check Solve the following Radical Equations

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

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.

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 .

Transformations of square-root functions are summarized below.

Describe the Transformation and the Domain and Range

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

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

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

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 .

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

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