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

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

3. Irrational algebraic function
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. Chapter 8: Irrational Algebraic Functions
Section 8-2:
Graphs of
Irrational
Functions

5. Objective
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. Graph the function
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. What went wrong? 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. Consider the following Example:
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?

9. HOMEWORK:
Finish Worksheet