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: (, ) Height of a Ball 3; The height of the ball at 0 seconds -1 second and 3 seconds 3 feet 1 second x < 1 second x >1 second (1,4) None

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 -4; She starts owing $4 2 glasses of lemonade $6; She makes 6$ with 5 glasses sold 6; She makes $8 selling 6 Glasses. Always Profit from Sally’s Lemonade Stand Profit ($) Number of Glasses Sold 7

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

Cost of Cab Rides Miles Fare ($) Company A A(x) = x + 5 Company B B(x) = 3x + 1 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 miles B is a better value until 2 miles. After two miles, A is a better value $5. Company A charges $5 for 0 miles $7 Company B charges $7 for 2 miles 1 mile 2 miles

xL Find and Interpret 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 Bags Profit Y1=2x ; He makes -2$ if he doesn’t sell any popcorn 1 bag of popcorn 1 8; if he sells 5 bags then he will make $8 3 bags 4; If he sells 4 bags then he will make $6 Next=Now + 2; starting at -2

D: 0< x < 13.5 R: 1 < y < 9.5 Yes; Each time has just one height. 3; The height is 3 ft after 0.5 seconds. 7.5; The height is 7.5 ft after 4.5 seconds. 6.5; The height is 6.5 ft after 8.5 seconds. 3) Find and interpret the y-intercept?________________________________ 3; The height is 3 ft after 0 seconds. 7) When is the graph increasing? ____________________________ 8) When is the graph decreasing? _____________________________ 9) What is the maximum height? _____________________________ 1< x < < x < 7.3 and 12< x < ft

D: 0< x < 15 R: 0.5 < y < 44 Yes; Every time has just one height. 12; The height is 12 meters after 2 seconds. 5; The height is 5 meters after 8 seconds. 8.5, 11.5; The height is 20 after 8.5 and 11.5 seconds No solution; It never reaches 46 meters. 46 isn’t between 0.5 and = 22 The height at 3 seconds plus 10

Stair Stories Climbed by Two Climbers A(x) =(1/2)x + 5 B(x) =x + 2 Time (minutes) Stories 1.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? 6 minutes 8 stories 5 stories at 0 minutes At 2 minutes

x 'L 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 # of Pompoms Profit Y = 3x ; She loses $7 if she doesn’t sell any. ~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 3; she makes $2 by selling 3 pompoms ~2.3; She makes $0 if she sells 2.3 pompoms.

xy1y Delivery Charges of 2 Companies A(x)B(x) A(x) = 2x + 3 B(x) = 2.5x + 1 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; B is better for less than 4 miles; A is better for more than 4 miles; 3; Company A charges $3 for no miles traveled 6; Company B charges $6 for 2 miles traveled X = 4 When x is 5 Next = Now + 2.5; starting at 1

Year Millions of Cars in US Find and interpret f(1955) 7.8 million, In 1955, there were 7.8 million cars 2. Find and interpret f(x) = ; In 2000, there were 17.4 milllion cars 3. When were there 11.5 million cars In the US? In 1980

Number of Starbucks Outlets 1.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) = In ~2006, there were 10,000 Starbucks

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