1. Compare Functions

2. 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 (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

3. 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

4. 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 – 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

5. 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

6. 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

7. 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

8. 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

9. 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