Refresher Rate of Change in the Real World

Name: ______Pd: 1 2 4 5 6 7 Date: 9/13/2015 13

Key terms Term Definition Example Rate of Change Ratio of the change in the output value and the change in the input value of a function. Slope

Refresher – Rate of Change in the Real World Felipe had to go run an errand before he could head home after school. The graph below follows his journey measuring distance from school over time. Complete the table identifying the domain, change in x, range, change in y, and a sentence explaining the rate of change. Hint: “As ___[indep. var.]____ increases by 1 unit, ___[dep. var.]___ increases/decreases by ____[rate of change]____.” R.o.C. Interpretation of R.o.C. 1

Slope Rate of Change = ------= ------= ------= Slope

We Do – Slope from Graphs (Real World) Example 1. The graph below 2. Jeremy goes to mall and buys clothes on a spending spree of shows the growth of Darin’s sorts. Identify the slope of the line. What does this mean? tree over many years. Identify the slope of the line. What does this mean?

We Do – Slope from Graphs We Do – Slope in Verbal Descriptions Example 3. Identify the slope of 4. Identify the slope of the line 5. Identify the meaning of the 6. Identify the meaning of the the line below. below. slope in the equation: slope in the equation: You just adopted a baby turtle. You work at Saks Fifth Avenue Your turtle is growing at a selling women’s shoes. Your constant rate. The turtle’s length, monthly income, y, in dollars, as L, in inches, as a function of his a function of how many shoes age, w, in weeks, is modeled by your customers buy, x, is the equation . modeled by the equation . Meaning of the slope: Meaning of the slope:

You Do Goal: ______% Do at least 11 out of the 16 problems. Make sure to use resources and check your work as you go! 1. Simplify: 2. Identify the slope of the line 3. Identify the slope of the line 4. Kayla makes extra money below. below. after school by mowing her neighbors’ lawns. The time, t seconds, that it takes Kayla to mow a lawn, is a function of the lawn’s area (in square feet), a, is modeled by the function . What is the slope of this equation, and what does it mean?

m = m = 5. Solve: 6. Identify the slope of the line 7. Identify the slope of the line 8. Identify the slope of the below. below. line below.

m = m = m = 9. Simplify: 10. Identify the slope of the 11. Calculate the slope from 12. Identify the slope of the line and its meaning. the table below. line and its meaning. X (days) Y (miles I ran) 3 7 4 9 5 11 The amount of

______increases

by ______per m = m = Meaning: Meaning: ______.

13. Solve: 14. Solve: 15. Shari works at a car 16. Write an expression that dealership. She earns a base matches the following pay, and then makes description: “eighteen less commission on each car she the product of x and four.” sells. Her annual pay, p, in dollars, is a function of how many cars she sells, c, modeled by the equation . What is the slope of this equation, and what does it mean?