FUNCTIONS We put the FUN in functions!!!!. Functions Definition: a relation in which each element of the domain is paired with exactly one element of.

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Presentation transcript:

FUNCTIONS We put the FUN in functions!!!!

Functions Definition: a relation in which each element of the domain is paired with exactly one element of the range. You decide: Yes or no? xy xy xy xy

Functions Is this a function?

Functions Is this a function?

Functions Domain: all the x values or input values for a function D = {1,2,3,4} Range: all the y values or output values for a function R = {3,5,7,9} xy

Functions We write functions a little differently than regular equations. f(x) = 15x f(x) is read the function of x The input x is any or f of x. It is the output or number. It is the domain. range value.

Function Notation Find f(4) for f(x) = 2x + 1 means What is the value of the function when x = 4. In this example you replace x in the equation with 4. f(x) = 2(4) +1 9 f(4) = 9

Find f(6) for f(x) = 2x + 1 means What is the value of the function when x = 6. In this example you replace x in the equation with 6. f(x) = 2(6) f(6) = 13

Find f(10) for f(x) = 2x +1 f(x) = 2(10) +1 f(10) = 21 Therefore f(10) = 21 We input 10 and the output is 21.

Find f(-7) for f(x) = 2x +1 f(x) = 2(-7) +1 f(x) = -13 Therefore f(-7) = -13 We input -7 and the output is -13.

Find f(-4) for f(x) = 2x +1 f(-4) = -7 Find f(-10) for f(x) = 2x +1 f(-10) = -19 Find f(3) for f(x) = -3x -8 f(3) = -17

Which will increase the volume of a cylinder more quickly: increasing the radius or increasing the height?

Functions The cylinder below has a radius of 1 inch and a height of 3 inches. Find its volume. What would happen to the volume if you increased the radius in one increments, but kept the height the same? Use the table for your data. Height (h)Volume (cubic in) 1 in 2 in 3in 4 in 5 in 6 in 7 in 8 in

Functions Is this a linear relationship? How do you know? Graph the relationship between radius and volume on your graph paper? At what radius would the volume be 100 cubic inches? How can you tell if the relationship is a function by looking at the table? By looking at the graph?

Hiking Trip Bruneau sand dunes hike: We walked 3/5 a mile in 3/4 of an hour and kept that same pace for the day. The following information comes from three different hiking trips the group went on last year. Can you identify how many miles per hour the groups hiked on each trip? Stanley Lake Hike Time Distance Traveled 7:00 – 8: miles 8:30 – 11:00 Graph from the Bogus Basin Hike