SFM Productions Presents: Another fulfilling episode of your continuing Pre-Calculus experience! 1.4Functions.

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1.4: Functions Objectives: To determine if a relation is a function

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SFM Productions Presents: Another fulfilling episode of your continuing Pre-Calculus experience! 1.4Functions

Homework for section 1.4 P , 45, 49, 51, 59-81, 89, 105, 106

What is a function? Equation that when you plug in some number for x, you only get one answer for y. Examples: are the following functions?

Many things involve two quantities that are related to each other - these are called relations. (duh) We can define a relation as a set of ordered pairs. The domain is the set of all the x-values (or coordinates) of a relation. (input) The range is the set of all the y-values (or coordinates) of a relation. (output)

InputOutputEquationFunction DomainRange xy xf(x) Independent Dependent Girls rule! Boys drool!

f is the name of the function f(x) is the value of the function (OUTPUT) Usually use the letters f and x, but other letters can be used. x is the number you INPUT into the function

Example What do you get when you plug in 1 for x? 3? 5? The new way is called: function notation. But it means the same thing. Now what I want to know is: What is f(1)? f(3)? f(5)?

Example It does not matter what you plug in for x…it’s always a direct substitution.

Functions can be defined by two or more equations. These are called: Piecewise-Defined Functions Example: This is what you do.This is where you do it.

Domains of a function can be stated explicitly. (don’t worry, it’s nothing dirty) Or, they may be implied by the expression used to define the function. Ready for this??? These are called Implied Domains. Implied Domains occur when you have the potential for division by 0, or when you have a negative number under an even root - ie, a square root.

Examples of each… What numbers can’t x be? What numbers can’t m be?

A softball is hit at a point 3 feet above the ground at a velocity of 100 fps at 45 o. The path of the ball is given by the following function: where both x and y are measured in feet. There is a 10 ft high fence 300 feet away. Does the ball clear the fence?

A softball is hit at a point 3 feet above the ground at a velocity of 45 fps at 70 o. The path of the ball is given by the following function: where both x and y are measured in feet. There is a 10 ft high fence 300 feet away. Does the ball clear the fence?

Difference Quotients (you’ll see it in Calculus) Evaluating a Difference Quotient… If What is the difference quotient?

Go! Do!