Section 8-1:

Introduction to

Irrational

Algebraic Functions

Chapter 8: Irrational Algebraic Functions

objective

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

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:

3 2f x x

Section 8-2:

Graphs of

Irrational

Functions

Chapter 8: Irrational Algebraic Functions

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.

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.

3 2f x x

What went wrong?

When solving the equation, we will get:

2 2x

Is this possible? Why or why not?

The number 2 is what we call an extraneous solution.

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?

3 4f x x x

HOMEWORK:

Finish Worksheet