Compare Functions

There are 4 ways a function can be communicated: Verbal: Mariah opened her savings account with $1,200. Each month she adds $50. Equation: y = 50x + 1200 (S-I Form or Standard Form) Where y represents the amount in Mariah’s account and x represents the number of months she made the deposit. Table: 4. Graph: Each one of these formats communicate the same information about Mariah and her savings account. Months (x) Amount in account (y) $1,200 1 $1,250 2 $1,300 3 $1,350 4 $1,400 5 $1,450

Compare Functions It’s usually easier to compare 2 different functions if they are written in the same format Compare equations with equations graphs with graphs tables with tables

Compare Equations f(x) = 2x + 7 and g(x) = -3x + 7 Same y intercepts (0,7) Different x intercepts (-3.5,0) and (21/3,0) Different slopes ( 2 and -3) so the lines will intersect f(x) = -4.5x – 13.5 and g(x) = -4.5x + 27 Different y intercepts (0,-13) and (0,28) Different x intercepts (-3,0) and (6,0) Same slopes (-4.5) so the lines are parallel

Compare Equations f(x) = 3x - 6 and g(x) = -4x + 8 Different y intercepts (0,-6) and (0,8) Same x intercepts (2,0) and (2,0) Different slopes ( 3 and -4) so the lines will intersect f(x) = 4x and g(x) = -1/4x + 12 Different y intercepts (0,0) and (0,12) Different x intercepts (0,0) and (48,0) Opposite Reciprocal slopes ( 4 and -1/4) so the lines will be perpendicular

Compare Functions It’s often harder to compare two functions when they are written in different formats. So gather the basic information to compare (ie. find slope of both and compare slopes, or find y-intercept of both to compare) Or you can write the equation for each one and then compare the equations

Video rental LATE fees for 2 different stores. Compare Functions Video rental LATE fees for 2 different stores. Store 1 Store 2 f(x) = 1.25x + 1 Where f(x) is the total late fee in dollars and x is the number of days late. Which store is cheaper for 2 days late? Store 1 g(2) = Store 2 f(2) = Which store is cheaper for 10 days late? Store 1 g(10)= Store 2 f(10)= Days Late Fee 1 $1.50 2 $3.00 4 $4.50 5 $6.00 Store 1 $3.00 $3.50 Store 2 $15.00 g(x)=1.5x $13.50 *tip: often useful to write the equation for both

Kip and Joan are members at different fitness clubs… Compare Functions Kip and Joan are members at different fitness clubs… Kip’s Gym Joan’s Gym Joan’s membership fee is $50 then she pays $10 per week. *tip: often useful to write the equation for both g(x)=10x+50 f(x)=20x+20 Who has the better deal for going to the gym for only one week? Kip’s cost for 1 week = Joan’s cost for 1 week = Who has the better deal after 8 weeks of having the membership? Kip’s cost for 8 weeks = Joan’s cost for 8 weeks = $40 Kip $60 $180 Joan $130

Compare Functions Which function represents the car with better gas mileage? Gas mileage of Car #2. Gas mileage of Car #1 is 16 miles per gallon. Compare Rate of Change: 16 miles per gallon is the rate of change The slope of the graph is the rate of change Slope = 10, so 10 miles per gallon Car #1 has better gas mileage b/c it gets more mpg