1. Section 8-1: Introduction to Irrational Algebraic Functions

2. Learn things about an irrational algebraic function by pointwise plotting of its graph and other algebraic techniques.

3. An irrational algebraic function is a function in which the independent variable appears under a radical sign or in a power with a rational number for its exponent. Example:

4. Section 8-2: Graphs of Irrational Functions

5. Given the equation of an irrational algebraic function, find f(x) when x is given and find x when f(x) is given and plot the graph.

6. Two interesting things happen when we evaluate the function: If you choose a value of x where x < -2, f(x) will be imaginary and thus not show up on the graph. Secondly, if you substitute a number such as f(x) = 1, and try to solve for x, we run into a problem. Let’s look what will happen.

7. When solving the equation, we will get: Is this possible? Why or why not? The number 2 is what we call an extraneous solution.

8. What is the least value of x for which there is a real number value of f(x)? Plot the graph of function f using a suitable domain. What does the f(x) intercept equal? What does the x intercept equal? Find two values of x for which f(x) = -5. Find one value of x for which f(x) = -3. Show that there are no values of x for which f(x) = -8. f(x) reaches a minimum value somewhere between x = -4 and x = 0. Approximately what is the value of x? Approximately what is the minimum value?

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