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SFM Productions Presents:Another fulfilling episode of your continuingPre-Calculus experience!1.4FunctionsHomework for section 1.4P 4825- 39, 45, 49, 51,59-81, 89, 105, 106What 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)InputOutputEquationFunctionDomainRangexy

xf(x)

IndependentDependentGirls rule!Boys drool!f is the name of the functionf(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 functionExample

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 xits always a direct substitution.

Functions can be defined by two or more equations.These are called: Piecewise-Defined FunctionsExample:

This is what you do.This is where you do it.Domains of a function can be stated explicitly.(dont worry, its 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 eachWhat numbers cant x be?

What numbers cant m be?

A softball is hit at a point 3 feet above the ground at a velocity of 100 fps at 45o. The path of the ball is given by the following function:

where both x and y are measured in feet. There is a10 ft high fence 300 feet away. Does the ball clear the fence?310300

A softball is hit at a point 3 feet above the ground at a velocity of 45 fps at 70o. The path of the ball is given by the following function:

where both x and y are measured in feet. There is a10 ft high fence 300 feet away. Does the ball clear the fence?310300Difference Quotients (youll see it in Calculus)

Evaluating a Difference Quotient

IfWhat is the difference quotient?

Go! Do!