(GPA, student) (area code, person) (person, shirt color)

Transcription

1 Foundations of Algebra Unit 5 Review Part One Name: Day One: Function Notation In order for a relation to be a function, every must have exactly one. 1) Determine whether each of the following represents a function. (GPA, student) (area code, person) (person, shirt color) 2) Use the following functions to answer the questions below. When using function notation, remember f(x)=y. g(x) = -3x + 1 f(x) = x h( x) 12 j( x) 2x 9 x g(10) = f(-3) = h(2) = x such that j(x)=23 x such that g(x)=70 x such that h(x)=-2

2 3) Use the graph below to answer the following questions. f(40) = f(10) = x such that f(x)=0 x such that f(x)=10 Day Two: Creating Functions 1)Identify the independent and dependent quantities of the below scenarios. Independent: Dependent: Independent: Dependent: 2) Write an equation to represent the following scenarios. Be sure to define all variables and include units with your answer. a) A cell phone company charges $30 per month plus $0.07 per minute. If Mr. T s January cell phone bill was $59.40, how many minutes did he talk? b) A water tank contains 600 gallons of water and is leaking at a rate of 15 gal/min. How long will it take for the tank to empty?

3 3) Write a linear equation in slope-intercept form to represent each of the following tables. Day Four: Slope 1) Identify the following graphs as having positive, negative, zero, or undefined slopes.

4 2) Find the slope for each relationship represented by the tables below. Include units. 3) Write the equation in slope-intercept form for the following graphs. Day Five: Slopes and Y-Intercepts 1) The equation y = x represents the distance in miles that Tyler has to travel in order to get home for x minutes. What is the y-intercept? What does it represent? 2) The equation y = 0.40x + 20 represents the total cost for x number of minutes on a cell phone plan. What is the slope? What does it represent?

5 3) The cost, in dollars, of printing n digital photos is n. What is the slope? What does it represent? What is the y-intercept? What does it represent? Day 6: Graphing Lines Graph the following equations.

6 Day 7: Converting Between Different Forms of Lines 1) Convert to slope-intercept form and 2) Find the x-intercept and y-intercept. then graph. Then graph. 2) Convert from standard form to slope intercept form. a) 2x + y = 4 b) 2x 4y = 12 Day 8 and 9: Characteristics of Functions Domain: Range: Maximum: Minimum: Interval of Increase: Interval of Decrease: Interval of Constant: Y-Intercept(s): X-Intercept(s): Zero(s):

7 Domain: Range: X-Intercept(s): Y-Intercept(s): Zero(s): Positive: Negative: Maximum: Minimum: Interval(s) of Increase: Interval(s) of Decrease: Interval(s) of Constant: As x, f(x) As x, f(x)

8 Day 10: Real World Characteristics 1) It has been observed that a particular plant's growth is directly proportional to time. It measured 2 cm when it arrived at the nursery and 2.5 cm each week. Independent Quantity: Domain: Dependent Quantity: Range: 2) A fishing lake was stocked with 300 bass. Each year, the population decreases by 25 bass. The population of bass in the lake after x years is represented by the function f(x) = x. Calculate the x and y intercepts and then interpret them in terms of the problem scenario. 3) Emily wants to purchase songs that are $2 apiece on itunes. She has $15 that she can spend. Independent Quantity: Domain: Dependent Quantity: Range:

9 Day 11: Writing Equations of Lines 1) Find the equation of the line that passes through the points given. a) (9,2) and (7,4) b) (5, -1) and (10, -5) c) (6, 10) and (9, 12) d) (1, -7) and (6, 3) e) Marciel rented a moving truck for the day. Marciel only remembers that the rental truck company charges $40 per day and some amount of cents per mile. Marciel drives 46 miles and the final amount of the bill (before tax) is $63. What is the amount per mile the truck rental company charges per day? Write an equation in slope intercept form that describes this situation. How much would it cost to rent this truck if Marciel drove 220 miles? f) Nadia is placing different weights on a spring and measuring the length of the stretched spring. She finds that for a 100 gram weight the length of the stretched spring is 20 cm and for a 300 gram weight the length of the stretched spring is 25 cm. Write an equation in slope intercept form that describes this situation. What is the unstretched length of the spring?

10 Day 12: Comparing Functions

11 Day 13: Arithmetic Sequences For the following, write the recursive and explicit rules/formulas, and then find the indicated term.