Y-intercept: Beginning value Where graph crosses y-axis X-intercept, Zeros, Break-even point: Where graph crosses x-axis f(2) : X-value is 2, find the y value f(x) = 4: y value is 4 find the x value Increasing: The x-values where the graph is going up Decreasing: The y-value where the graph is going down Maximum: ( , ) Minimum: ( , ) 3; The height of the ball at 0 seconds Height of a Ball -1 second and 3 seconds 3 feet 1 second x < 1 second x >1 second (1,4) None

-4; She starts owing $4 2 glasses of lemonade 2 glasses of lemonade Y-intercept Find Break-even point: X-intercept Find and interpret f(5) : Find and interpret f(x) = 8: Increasing: Solve by the graph: 2x – 4 = 10 Profit from Sally’s Lemonade Stand -4; She starts owing $4 2 glasses of lemonade Profit ($) 2 glasses of lemonade $6; She makes 6$ with 5 glasses sold 6; She makes $8 selling 6 Glasses. Always Number of Glasses Sold 7

Projected Profit of Concert Based on Ticket Price Initial Value: Break-even point: Find and interpret f(2) : Find and interpret f(x) = 40: Increasing: Find and interpret the maximum: When is -4x2 – 40x – 50 = 20? They lose $5000 if ticket price is $0 Projected Profit of Concert Based on Ticket Price They start making money with Ticket price of $1.50 Profit (Hundred’s of Dollars) They make ~$1800 with a Ticket price of $2 They make $4000 with a ticket price of $3.50 or $6.50 x < $5. Cost of Ticket ($) (5,50); Maximum profit is $5000 when ticket price is $5 At x = $2.10 and $7.8

2. Find and interpret the y-intercept Number of Starbucks Outlets Find and interpret f(2000) ~5000. In 2000, there were 5000 Starbucks 2. Find and interpret the y-intercept In 1970 there were about 1 Starbucks 3. Find and interpret f(x) = 10000 In ~2006, there were 10,000 Starbucks

Fare ($) Cost of Cab Rides Miles 2 miles After how many miles will the companies be the same? Explain when each company is a better value. Find and interpret the y-intercept of A(x) and what does it mean? Find and Interpret B(2) When is 3x + 1 = 4? When is 3x + 1 = x + 5 Cost of Cab Rides 2 miles Company A A(x) = x + 5 B is a better value until 2 miles. After two miles, A is a better value Fare ($) $5. Company A charges $5 for 0 miles Company B B(x) = 3x + 1 $7 Company B charges $7 for 2 miles 1 mile 2 miles Miles

6 minutes 8 stories Stair Stories Climbed by Two Climbers What time will they have climbed the same amount of stories? 2. How many stories will they have climbed? 3. Find and interpret the y-intercept of person A? 4. When x+2 = 4? Stair Stories Climbed by Two Climbers 6 minutes A(x) =(1/2)x + 5 Stories 8 stories B(x) =x + 2 5 stories at 0 minutes At 2 minutes Time (minutes)

Find and Intrepret Y-intercept Find Break-even point: X-intercept Find and interpret f(5) : Find and interpret f(x) = 6: Solve by the table: 2x – 2 = 4 Write the NEXT-NOW equation Profit of Selling Popcorn -2; He makes -2$ if he doesn’t sell any popcorn Bags Profit x L1 0 -2 1 0 2 2 3 4 4 6 5 8 1 bag of popcorn 1 8; if he sells 5 bags then he will make $8 Y1=2x - 2 4; If he sells 4 bags then he will make $6 3 bags Next=Now + 2; starting at -2

x 'L1 -1 -10 0 -7 1 -4 2 -1 3 2 4 5 Find and interpret y-intercept Find and interpret Break-even point: Find and interpret zeros Find and interpret f(4) : Find and interpret f(x) = -4: Solve by the graph: 3x – 7 = 2 Profit of Selling Pompoms -7; She loses $7 if she doesn’t sell any. # of Pompoms Profit ~2.3; She makes $0 if she sells 2.3 pompoms x 'L1 -1 -10 0 -7 1 -4 2 -1 3 2 4 5 ~2.3; She makes $0 if she sells 2.3 pompoms. 5; She makes 5$ for selling 4 pompoms 1; She loses 4$ for selling 1 pompom Y = 3x - 7 3; she makes $2 by selling 3 pompoms

Delivery Charges of 2 Companies After how many miles will the companies be the same? Explain when each company is a better value. Find and interpret the y-intercept of A(x) and what does it mean? Find and Interpret B(2) When is 2x + 3 = 2.5x + 1 When is 2x + 3 = 13? Write the NEXT-NOW equation for B(x) 4 miles; Delivery Charges of 2 Companies B is better for less than 4 miles; A is better for more than 4 miles; A(x) B(x) x y1 y2 0 3 1 1 5 3.5 2 7 6 3 9 8.5 4 11 11 5 13 13.5 6 15 16 3; Company A charges $3 for no miles traveled 6; Company B charges $6 for 2 miles traveled X = 4 When x is 5 A(x) = 2x + 3 Next = Now + 2.5; starting at 1 B(x) = 2.5x + 1

Year Millions of Cars in US 1950 6 1955 7.8 1960 7.3 1965 10.3 1970 10.1 1975 10.8 1980 11.5 1985 15.4 1990 13.5 1995 15.5 2000 17.4 2005 16.9 Find and interpret f(1955) 7.8 million, In 1955, there were 7.8 million cars 2. Find and interpret f(x) = 17.4 2000; In 2000, there were 17.4 milllion cars 3. When were there 11.5 million cars In the US? In 1980

Starting Value Rate Increase or Decrease Decimal multiply by NEXT=NOW Statement 1st 4 Numbers $20,000 5% increase 100+5 = 105% =1.05 Or 1(20,000) + .05(20,000) Next=Now*1.05 starting at 20,00 5 % decrease $100 4% interest 95,000 3.5% increase 8,6,4.5, Next = Now *1.095 starting at $1000 12,20,100/3 x 15% commission 20000, 21000, 22050, 23152.50 100-5 = 95 = .95 Next = Now *.95 5 starting at 20000 20000, 19000, 18050, 17147.50 Next = Now *1.04 starting at 100 100,104,108.16, 112.49 100+4 = 104 =1.04 100+3.5 = 103.5= 1.035 Next = Now *1.035 starting at 95000 95000, 98325, 101767, 105328 8 0.75 Next = Now *.75 Starting at 8 25% decrease 6/8 = .75 1000 1000,1095, 1199, 1312.93 1.095 9.5% increase 12 66.7% increase Next = Now *1.667 Starting at 12 1.667 20/12 = 1.67 .15