# 3.5 – Functions and Tables

Objectives

• Find a function’s domain and range values in an input-output table
• Interpret data from an input-output table to solve an inequality
• Use an input-output table to estimate more values of a function
• Use an input-output table to find the rule for a function

Key Terms

• Input-Output Table – A two-column table whose first column contains input (domain) values of a function and whose second column contains output (range) values.

Notes

• Look at the inputs and see if you can recognize a rule for the function.
• Look at the outputs and see if you can recognize a rule for the function.
• How much does y increase when x increase?
• Remember, y depends on x

•  Example 1

• Notice that 1 Gallon of Gas is $2.15 and 2 Gallons of Gas is$4.30.
• If you divide the range by the domain (y by x), you get $2.15 for every pair. Try it! • $\frac{10.75}{5}=2.15$ • This is the same as 2.15 times x. • So, now that you know the function is F(x) = 2.15x, you can put in any number or Gallons to find out what the total cost would be. • F(15) = 2.15(15) =$32.25!

• Example 2: Tax on an Item
• You may own your own business one day selling something you make (cookies, fashion, jewelry, car decals, who knows!).
• You will need to collect taxes on each item you sell so that you can pay your own taxes at the end of the year. What if you don’t collect enough taxes? You’ll end up owing more money than you made! That would be awful!
• So, how can you tell which tax amount is the wrong?
• What is the tax on $1? • 1 is a good number to use as a base, as all larger items (and amounts) can be broken down into single units (or amounts). • Notice that the tax on$1.00 is 0.08 cents. Let’s use that as our function:
F(x) = 0.08x
F(1) = 0.08(1) = 0.08
F(2) = 0.08(2) = 0.16
F(3) = 0.08(3) = 0.24
F(8.50) = 0.08(8.50) = 0.68
F(10) = 0.08(10) = 0.80
• So, which one, from the table provided (above) is incorrect?
• $8.50 should have a tax of 0.68 cents, not 0.64 cents! • Example 3: Miles to Go • If you start at 0 miles, you have 630 miles to go til you get to your destination. • Notice that the total trip – miles traveled = miles to go • x: miles traveled • y: miles to go • So, 630 – x = y • After 100 miles: 630 – 100 = 530 • After 420 miles: 630 – 420 = 210 • Example 4: Job Training • When you start a job, even before you get training, they will pay you for working. • When you start working, without any training, what will you make per month? • After 10hrs of training, you make$1220
• After 20hrs of training, you make $1420 • So, for every 10hrs of training, you make$200 more dollars per month!
• When you were hired, you made $200 less than you would before your first 10hrs of training.$1220 – $200 =$1020.

• How much do you make for EACH hour you train?
• 10h = $200. To find 1hr, divide both sides by 10. • $\frac{10h}{10}=\frac{200}{10}$ • $h=20$ • So, for 1 hour of training, you’ll get paid$20.
• If you want to make $1500 a month, how much training should you get? Remember, you get a base pay of$1020 plus $20 for every hour of training. • 1020 + 20h = monthly pay • $1020+20h=1500$: subtract 1020 on both sides • $20h=480$: divide both sides by 20 • $\frac{20h}{20}=\frac{480}{20}$ • $h=24$: You will need to train for 24 hours to make$1500 a month.