Skills Practice. I. Identifying Independent and Dependent Quantities

Transcription

1 Skills Practice I. Identifing Independent and Dependent Quantities A. Determine the independent and dependent quantities in each scenario. Be sure to include the appropriate units of measure for each quantit. 1. Selena is driving to visit her grandmother who lives 35 miles awa from Selena s home. She travels an average of 0 miles per hour.. Benjamin works at a printing compan. He is making T-shirts for a high school volleball team. The press he runs can imprint 3 T-shirts per minute with the school s mascot. 3. On her wa to work each morning, Sophia purchases a small cup of coffee for $.5 from the coffee shop.. Phillip enjos rock climbing on the weekends. At some of the less challenging locations he can climb upwards of 1 feet per minute. 5. Jose prefers to walk to work when the weather is nice. He walks the 1.5 miles to work at a speed of about 3 miles per hour.. Gavin works for a skdiving compan. Customers pa $00 per jump to skdive in tandem skdives with Gavin. : Skills Practice 1

2 B. Label the aes of each graph with the independent and dependent quantities and the appropriate unit of measure. 1. Madison enjos biccling for eercise. Each Saturda she bikes a course she has mapped out around her town. She averages a speed of 1 miles per hour on her journe.. Natasha is filling the bathtub with water in order to give her dog Buster a bath. The faucet fills the tub at an average rate of 1 gallons per minute. Distance Madison Bikes Amount of Water in Bathtub 0 0 MODULE 1: Searching for Patterns

3 3. Marcus throws a football straight up into the air. After it reaches its maimum height of 0 feet, it descends back to the ground.. Chloe is using a pump to drain her backard pool to get read for winter. The pump removes the water at an average rate of 15 gallons per minute. Football Height Amount of Water in Pool 0 0 : Skills Practice 3

4 5. Jermaine is saving mone to purchase a used car. He places $50 dollars in a savings account that earns 1.5% interest annuall.. Zachar enjos hiking. On the first da of his latest hiking trip, he hikes through flat terrain for about miles. On the second da, he hikes through ver steep terrain for about 3 miles. On the third da he hikes through some hill terrain for about miles. Value of Investment Distance Hiked 0 0 MODULE 1: Searching for Patterns

5 II. Identifing Domain and Range A. Identif the domain and range of each situation using words and inequalities. 1. Victoria recentl switched to a new electric compan. If she uses between 0 and 00 kilowatt-hours (kwh) of electricit per month, the cost is a set price of $30. If she uses 00 kwh or more per month, the price is $0.097 per kwh.. Rohan is at an amusement park. While waiting in line, he reads the statistics on the roller coaster he is about to board. The coaster reaches a maimum speed of 75 miles per hour, and the ride lasts three minutes. 3. Graham uses a hot water bottle on an injur to his back he incurred plaing basketball. He fills the bottle with water that is a temperature of 100 F. After 5 minutes, Graham finds that the bottle has cooled and he stops using it.. Lenore is going to sell T-shirts at a field hocke game to raise mone for the team. She finds a website that makes custom T-shirts. The compan charges $11.99 per shirt for an order less than 50, $9.99 per shirt for 50 to 100 T-shirts, and $7.99 for more than 100 T-shirts. 5. A township bus a new asphalt road paver. The paver costs $50,500. The value of the paver decreases each ear after purchase. Eventuall, it decreases so much in value that it can onl be sold for $,500 for parts.. Peton is training to run a half-marathon. One night, she runs a total of 10 miles. She runs the first miles at a pace of miles per hour, the net 5 miles at a pace of 7 miles per hour, and the last mile at a pace of miles per hour. : Skills Practice 5

6 7. Kala is blowing up balloons for her sister s birthda part. She tries to blow up each balloon to a maimum diameter of 5 inches. At that diameter, the volume of each balloon is about cubic inches.. Neville and his friends are going to a local peach festival. The plan to go on rides all da. The tickets for the rides are $0.50 each. 9. When his first granddaughter is born, Marik invests $5,000 in savings bonds. He plans to cash in the bonds when his granddaughter turns 1 to help pa for her first ear of college. 10. A compan manufactures boes of macaroons. The incur a fied manufacturing cost of $,000, as well as a variable cost of $1.75 for each bo of macaroons. The compan onl has the capacit to make up to 00 boes of macaroons a week. 11. Kea is kaaking on a river. The cost to rent the kaak is $5 per hour or $00 for the entire da, from a.m. to p.m. 1. Tavares has a thermos that he takes to volleball practice. The thermos can hold up to 1 ounces of water. The thermos develops a leak and starts losing water at a rate of 1 ounce ever minutes. MODULE 1: Searching for Patterns

7 III. Identifing Characteristics of Graphs A. Sort the graphs into groups. Write the letter of the graph in the group bo. (Some graphs belong to more than one group.) 1. Function Maimum or Minimum Increasing Onl Decreasing Onl Graph A Graph B 0 0 : Skills Practice 7

8 Graph C Graph D 0 0 Graph E Graph F 0 0 MODULE 1: Searching for Patterns

9 Graph G Graph H 0 0 Graph I Graph J 0 0 : Skills Practice 9

10 Graph K Graph L 0 0 IV. Identifing Functions A. Determine which relations represent functions. If the relation is not a function, state wh not. 1.. Domain Range MODULE 1: Searching for Patterns

11 Domain Range : Skills Practice 11

12 B. Rewrite each function using function notation. 1. Rewrite the function 5 3 using function notation so that the dependent quantit, defined as f, is a function of the independent quantit. 3. Rewrite the function using function notation so that the dependent quantit, defined as P, is a function of the independent quantit. 5. Rewrite the function d 5 1 m 1 5 using function notation so that the dependent quantit, defined as A, is a function of the independent quantit m.. Rewrite the function using function notation so that the dependent quantit, defined as C, is a function of the independent quantit.. Rewrite the function l 5 n using function notation so that the dependent quantit, defined as L, is a function of the independent quantit n.. Rewrite the function c 5 pr using function notation so that the dependent quantit, defined as C, is a function of the independent quantit r. V. Recognizing Function Families A. Determine whether each graph represents a linear function, a quadratic function, an eponential function, a linear absolute value function, or a linear piecewise function MODULE 1: Searching for Patterns

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15 VI. Identifing Function Characteristics A. Create an equation and sketch a graph for a function with each set of given characteristics. Use values that are an real numbers between 10 and Create an equation and sketch a graph that: is a smooth curve, is continuous, has a minimum, and is quadratic.. Create an equation and sketch a graph that: is linear, is discrete, and is decreasing across the entire domain : Skills Practice 15

16 3. Create an equation and sketch a graph that: is a smooth curve, is increasing across the entire domain, is continuous, and is eponential.. Create an equation and sketch a graph that: has a maimum, is continuous, and is a linear absolute value function MODULE 1: Searching for Patterns

17 5. Create an equation and sketch a graph that: is linear, is continuous, is neither increasing nor decreasing across the entire domain, and does not pass through the origin.. Create an equation and sketch a graph that: is discrete, has a maimum, does not pass through the origin, and is quadratic : Skills Practice 17