Lecture 2: Properties of Functions

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Presentation transcript:

Lecture 2: Properties of Functions

Domain & Range Domain: The domain of a function is the set of all the possible values of the independent variable (all the possible x-values) of your function.

Domain & Range e.g. Domain : [-3 , 4]

Domain & Range Domain: [-4, -2] U [1,5]

Domain & Range Range: The range of a function is the set of all the possible values of the dependent variable (all the possible y-values) of your function.

Domain & Range e.g. Range: [-5 , 3]

Domain & Range e.g. ]5,11] U 1 [0,4] Range: [0 , 4] U ]5, 11]

Variations “Variations” describe what is happening to function: i.e. Under which domain intervals does the function increase, decrease, or stay constant. NOTE: The way I described this in class last week was very different from the description the book gives so please pay attention. I made a mistake apparently.

Variations A function is increasing if it is represented by a line or curve that is ascending (going up) from left to right or constant!!!. e.g. Increasing: [-3, 3]

Variations A function is decreasing if it is represented by a line or curve that is descending (going down) from left to right or constant!!!. e.g. Decreasing: [-2, 6]

Variations A function is constant if it is represented by a horizontal line (going straight) from left to right. e.g. Constant: [-2, 3]

Extrema: Minimum & Maximum The Minimum of a function is the smallest value of the dependent variable. (Smallest y-value) The Maximum of a function is the largest value of the dependent variable. (Largest y-value)

Extrema: Minimum & Maximum e.g. Minimum: y = -4 Maximum: y = 5

Sign of the Function: +’ve and –’ve Using x-intervals….. A function is Positive if the values of the dependent variable are positive. A function is Negative if the values of the dependent variable are negative.

Sign of the Function: +’ve and –’ve e.g. Positive: [ -5 , -3 ] U [ 4 , 6] Negative: [-3 , 4 ]

Sign of the Function: +’ve and –’ve The Zero(s) of a function are the x-values where the function crosses the x-axis. Zeros: x = -3 & x = 4

Sign of the Function: +’ve and –’ve The Initial Value of a function are the x-values where the function crosses the y-axis. Initial value: y = -3