back to unit 2 page  range from equation
Range from a graph:
Range is the set of y values that the function uses. List the bottom value, then the top value. It uses a parentheses ( ) if the value is an infinity symbol,or a square bracket [ ] if it is a number value that is included in the range.
Piecewise function: The space used by the graphed function goes from 4 on the y axis to 3 on the y axis. The range is [4,3]. 
Quadratic function: The space used by the graphed function heads to  ∞ on the bottom to 2 on the top. The range is ( ∞,2]. 


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Polynomial: You are looking for the lowest bottom and highest top when you write up the range. Check the left and right sides to see what infinities they head towards. Here, both head to positive infinity so that's the top. The lowest graphed part bottoms at 1. The range is [1, ∞). 
Exponential: The graph will have a long flat portion that approaches a y value without reaching it (called horizontal asymptote). The other end will head towards an infinity. Here, the horizontal asymptote is at 1 and it heads to postive infinity. The range is (1, ∞). 


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Logarithms are the inverse functions of exponential functions.They have a vertical asymptote which limits domain. There is no limit on range. Write ( ∞,∞) for range. Graphed functions can be confusing because one side is so flat, but it keeps gradually creeping up or down forever. 
Rationals break into pieces, so you write the range with restrictions. The restrictions are the y values it doesn't use. Here,it will use all y values except 0. Write it up as a horizontal asymptote. Horizontal asmyptote at y=0. 


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