Download presentation

Presentation is loading. Please wait.

Published byMacey Millson Modified over 3 years ago

1
Splash Screen

2
Then/Now I CAN solve and estimate solutions to equations by graphing. Note Card 3-2A Define Linear Functions, Parent Function, Family of Graphs, Root, and Zeros. Note Card 3-2B Copy the Key Concept (Linear Function). Class Opener and Learning Target

3
Linear Function Definitions 3-2A Linear Function – a function with a graph of a line. Parent Function – the simplest linear function f(x) = x of a family of linear functions. Family of Graphs – a group of graphs with one or more similar characteristics. Root - solution – any value that makes an equation true. The root of an equation is the value of the x-intercept. Zeros – values of x for which f(x) = 0. The zero is located at the x-intercept of a function.

4
Concept Linear Function 3-2B

5
Example 1 A Solve an Equation with One Root A. Answer: The solution is –6. Subtract 3 from each side. Original equation Multiply each side by 2. Solve. Method 1 Solve algebraically.

6
Example 1 B Solve an Equation with One Root B. Find the related function. Set the equation equal to 0. Method 2Solve by graphing. Original equation Simplify. Subtract 2 from each side.

7
Example 1 B Solve an Equation with One Root Answer: So, the solution is –3. The graph intersects the x-axis at –3. The related function is To graph the function, make a table.

8
A.A B.B C.C D.D Example 1 CYPA A.x = –4 B.x = –9 C.x = 4 D.x = 9

9
A.A B.B C.C D.D Example 1 CYP B A.x = 4;B.x = –4; C.x = –3;D.x = 3;

10
Example 2 A Solve an Equation with No Solution A. Solve 2x + 5 = 2x + 3. Answer: Since f(x) is always equal to 2, this function has no solution. 2x + 2 = 2xSubtract 3 from each side. 2x + 5 = 2x + 3Original equation 2 = 0Subtract 2x from each side. The related function is f(x) = 2. The root of the linear equation is the value of x when f(x) = 0. Method 1 Solve algebraically.

11
Example 2 Solve an Equation with No Solution B. Solve 5x – 7 = 5x + 2. Answer: Therefore, there is no solution. 5x – 9 = 5xSubtract 2 from each side. 5x – 7 = 5x + 2Original equation –9 = 0Subtract 5x from each side. Graph the related function which is f(x) = –9. The graph of the line does not intersect the x-axis. Method 2 Solve graphically.

12
A.A B.B C.C D.D Example 2 CYP A A.x = 0 B.x = 1 C.x = –1 D.no solution A. Solve –3x + 6 = 7 – 3x algebraically.

13
A.A B.B C.C D.D Example 2 CYP B B. Solve 4 – 6x = – 6x + 3 by graphing. A.x = –1B.x = 1 C.x = 1D.no solution

14
Example 3 Estimate by Graphing FUNDRAISING Kendras class is selling greeting cards to raise money for new soccer equipment. They paid $115 for the cards, and they are selling each card for $1.75. The function y = 1.75x – 115 represents their profit y for selling x greeting cards. Find the zero of this function. Describe what this value means in this context. The graph appears to intersect the x-axis at about 65. Next, solve algebraically to check. Make a table of values.

15
Example 3 Estimate by Graphing Answer: The zero function is about 65.71. Since part of a greeting card cannot be sold, they must sell 66 greeting cards to make a profit. 0 = 1.75x – 115Related function y = 1.75x – 115Original equation 115 = 1.75xAdd 115 to each side. 65.71 xDivide each side by 1.75.

16
A.A B.B C.C D.D Example 3 A. 3; Raphael will arrive at his friends house in 3 hours. B.Raphael will arrive at his friends house in 3 hours 20 minutes. C.Raphael will arrive at his friends house in 3 hours 30 minutes. D. 4; Raphael will arrive at his friends house in 4 hours. TRAVEL On a trip to his friends house, Raphaels average speed was 45 miles per hour. The distance that Raphael is from his friends house at a certain moment in the trip can be represented by d = 150 – 45t, where d represents the distance in miles and t is the time in hours. Find the zero of this function. Describe what this value means in this context.

Similar presentations

OK

Section 4.2 Solving Linear Inequalities Using the Multiplication-Division Principle.

Section 4.2 Solving Linear Inequalities Using the Multiplication-Division Principle.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on power system harmonics analysis Ppt on edge detection test Ppt on double entry system Free ppt on history of cricket Free ppt on brain machine interface application Download ppt on oxidation and reduction in chemistry Ppt on anti bullying Ppt on face recognition technology using matlab Chemistry ppt on water Ppt on second law of thermodynamics explained