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Slide 1:

General Function Rules Input =x values (Domain) Output =y values (Range) “A relation is a function provided that there is exactly one output for each input.” ex . Input Output -3 3 1 -2 4 1 4 This is not a function because the input 1 has both the output of -2 and 1. ex . Input Output -3 3 1 1 3 -2 4 This is a function because each input has one output. ~ Vertical Line Test “A relation is a function if and only if no vertical line intersects the graph of the relation at more than one point.“ ~Identifying Functions

Slide 2:

y= mx+b Linear Functions y=x+1 Domain : all real #s Range : all real #s Slope: m= y 2 -y 1 =rise x 2 -x 1 run X Y -2 -1 -1 0 0 1 1 2 2 3

Slide 3:

Absolute Value Functions y= a|x -h|+k ~vertex: (h,k) ~V-shaped ~opens up when a>0 (see ex. 1) ~opens down when a<0 (see ex.2) ~graph is narrower if |a|>1 (see ex. 1) ~graph is wider if |a|<1 (see ex.2) ex. 1 f(x)= |2x| D: R: > 0 ex. 2 f(x)=- ½ |x+4|+6 D: R: < 6

Slide 4:

3 10 feet 5 feet y x If you hit the 3 ball at (4,4)and it hits the edge at (6,0) will the 3 ball make it in to the goal at (10,5)?

Slide 5:

Greatest Integer Function (Step Function) f(x)=[[x]] ~# outside [[]] =shift up or down ~# inside [[]] =shift sideways ~multiply # inside [[]] =bar shrinks or extends ~multiply # outside [[]]= space between bars increase by multiples of that number ex. 1 f(x)=[[x-1]] ex. 2 f(x)=[[ ½ x]] D: R: Integers D: R:

Slide 6:

Piecewise Functions ~A combination of equations ~One equation gives the value of f(x) when x < a ~The other equation gives the values of f(x) when x>a Some examples of a piecewise function are greatest integer and step function. f(x)= -x+2, if x < 0 3x-3, if x>0 D: R:

Slide 7:

Polynomial Functions ~Leading coefficient = a 0 (constant term) ~n=degree Y=x 4 -4.25x ² +1 D: R: y > -3 D: R: D: R:y > -9 Degree Types Standard Form 0 Constant f(x)=a 0 1 Linear f(x)=a 1 x+a 0 2 Quadratic f(x)=a 2 x 2 +a 1 x+a 0 3 Cubic f(x)=a 3 x 3 +a 2 x 2 +a 1 x+a 0 4 Quartic f(x)=a 4 x 4 +a 3 x 3 +a 2 x 2 +a 1 x+a 0 f(x)=a n x n +a n-1 x n-1 +…+a 1 x+a 0

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End Behavior For a n >0 and n is even, f(x)→+∞as x→-∞ and f(x)→+∞as x→+∞ For a n >0 and n is even, f(x)→-∞as x →-∞ and f(x)→+∞as x→+∞ For a n >0 and n is even, f(x)→-∞as x →-∞ and f(x)→-∞as x→+∞ For a n >0 and n is even, f(x)→+∞as x →-∞ and f(x)→-∞as x → +∞ of a polynomial function

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