Module 1  Describing Functions  
Introduction  Lesson 1  Lesson 2  Lesson 3  Self Test  
Lesson 1.1: Describing Functions Symbolically  
In this lesson you will define a function symbolically in the Y= editor and investigate the function on the Home screen. Defining a Function The function you will define is f(x) = 2x^{2}  5x  3.
Evaluating a Function Now that you have successfully defined the function f(x) = 2x^{2}  5x  3 in Y_{1}, you can evaluate the function at x = 2 by evaluating the expression Y_{1}(2) on the Home screen.
Editing the Last Entry If you want to evaluate the function at x = 3 next, you can recall and edit the last expression on the Home screen rather than entering in the entire expression.
Finding Zeros of Functions
One of the
1.1.1 Evaluate the function at other values of x until you find the other zero. When you have found the other zero, click here for the answer. Guess and Check
When you tried several values until you found the second zero, you used a method called
The Guess and Check method can be used to find zeros (or roots)of a function. Use the "Guess and Check" method to find the zeros of a function as follows:
First guess a value for the independent variable and evaluate the function there.
If the value of the function is not zero, pick another value of the independent variable and evaluate the function again. Considering the results from previous guesses might improve your later guesses
Continue in this manner until a zero is found.
The Relationship Between Zeros and Factors Many polynomial expressions, like 2x^{2}  5x  3, can be factored and there is a relationship between the zeros and the factors of the function. 1.1.2 Find the zeros of f(x) = 2x^{2}  5x  3 by factoring. Compare the zeros of the factors to the zeros of the function f(x) = 2x^{2}  5x  3 found earlier. Click here for the answer. For polynomial functions. x = r is a zero of f if and only if x  r is a factor of f(x). 

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