EC - Salary Graphs Lesson
Salary Graphs
Linear and Piecewise Functions
Graphs can be used to see a visual of different salary situations. Linear functions are often used in hourly pay scenarios. Recall that a function means that every input only maps to one output. Earning scenarios work this way as well. If you work a certain amount of hours, you couldn't earn two different payments. Let's take a look at how graphs can help visualize compensation scenarios.
The following graph shows Ariana’s pay based on the number of hours that she works in a pay period.
What do you notice about the slope of the line? At which hour does Ariana's pay change? How much extra does Ariana get when she works overtime?
Answer: The line for overtime has a steeper slope. Ariana's pay changes once she works over 40 hours. She receives time and a half, or 1.5 times her salary (12 * 1.5 = 18).
Robbie works at the Break-n-Fix repair company and earns $45 for a service call that involves up to and including one hour of labor. For each additional half-hour of labor, he earns $20. The hours of labor are always rounded up.
Between what time interval does Robbie earn $65? What does Robbie earn if he works for 2 hours and 15 minutes?
Answer: Robbies earns $65 dollars when he works between 1 hour and 1.5 hours. Robbie will earn $105 if he works for 2 hours and 15 minutes.
Domain and Range
The domain is the set of all possible values for the independent value or the x-value.
The range is the set of all possible values for the dependent value or the y-value.
Let’s say that Ariana’s company has a policy that employees cannot work more than 50 hours a week. Determine the domain and range of this situation.
Answer: The least Ariana could work is 0 hours, which would result in the least she could get paid, $0. The most that Ariana could work is 50 hours. If she works 50 hours, she would be paid 40 hours at her regular pay (12 x 50 = 480) and 10 hours at her overtime rate (18 x 10 = 180). This would result in the highest amount that she could earn, 480 + 180 = 660.
Domain (hours): 0 < x < 50
Range (pay): 0 < y < 660
Robbie’s situation differs from Ariana’s because this is not a continuous graph. Ariana can be paid in fractions of dollars, whereas Robbie’s earnings make jumps or “steps.” This can be referred to as a stepwise function, or greatest integer function. The range here contains only the specific values that Robbie can earn per service visit. Let’s say that there is a cap of 4 hours per service visit. Determine the domain and range of this situation.
Answer: The least Robbie could work is 0 hours, which would result in the least he could get paid, $0. Robbie can work up to 4 hours a visit in which he would earn $165. The range will look different in this scenario since there is a set of specific values that Robbie can earn.
Domain (hours): 0 < x < 4
Range (pay): y = {0, 45, 65, 85, 105, 125, 145, 165}
Comparing Graphs
Graphs can come in handy when comparing two different salary scenarios. Let's say you have been offered a choice of either working at an hourly rate of $18 an hour or accepting a flat rate of $450. Let's graph these two scenarios.
Which line represents the flat rate? Which represents the hourly rate? At which point will both payment options result in the same amount of money? Which should you choose if you believe the kob will take you about 20 hours?
Answer: The red line represents the flat rate and the red line represents the hourly rate. At hour 25, both options would result in the same amount of money. If the job will take about 20 hours, then the flat fee of $450 would be the better payment option.
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