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In this lesson we’ll be covering how to set-up piecewise defined functions based on story problems. Keep in mind that each piece of a piecewise defined function has its own domain, so we’ll also have to set-up an interval for each piece, just like the sample piecewise function given below:
3.3 Piecewise Functions . 1. Use the piecewise function to evaluate the following. 𝑓(𝑥) = 3 𝑥−2, 𝑥< −3 2𝑥. 2. −3𝑥, −3 < 𝑥≤6 8, 1 𝑥> 6. 2. Graph the following piecewise function. 𝑓(𝑥) = − 1 3 𝑥−2, 𝑥≤0 2 𝑥+ 1, 𝑥> 0
piecewise_functions_word_problems - Free download as PDF File (.pdf) or read online for free.
Evaluate the function for the given value of x. Match the piecewise function with its graph. Write the answer next to the problem number.
A certain county has a tax code, where 10% tax is paid on all income up to the rst $10,000, a 15% tax is paid for any income over $10,000 and up to $15,000, and a tax rate of 25% is paid on all income over $25,000. Find a piecewise function to calculate the total tax T (x) on an income of x dollars. Solution.
a. Write a piecewise function that relates the salesperson total monthly income based off or his/her sales for the month. b. Sketch an accurate graph of this piecewise function c. Determine the salesperson’s monthly income if his/her sales were $43,000 for the month. 2.
You have a summer job that pays time and half for overtime. That means, if you work more than 40 hours in a week, your hourly wage for the extra hours in 1.5 times your normal rate of $7 per hour. Write a piecewise function describing your weekly pay, P in term of the number of hours worked, h.
