Reteaching. Relating Graphs to Events

Transcription

1 3- Relating Graphs to Events The graph at the right shows the outside temperature during 6 hours of one da. You can see how the temperature changed throughout the da. The temperature rose 0 F from A.M. to 8 A.M. The temperature remained at 60 F for hours, from P.M. to P.M. The graph at the right shows a train moving between stations. The train moves slowl while leaving the station. Then it picks up speed until it reaches a cruising speed. It slows down as it approaches the next station and graduall comes to a stop. Since the graph is sketched to show relationships, the axes do not need number scales. But the axes and the parts of the graph should have labels to show what the represent. The graph at the right shows the altitude of an airplane during a flight. Use the graph for Exercises 3.. What was the airplane s altitude for most of the flight?. How long did it take the airplane to reach an altitude of,000 ft? 3. The third segment in the graph is not as steep as the first segment. What does this mean? Sketch and label a graph of the relationship.. You enter the freewa in our car, steadil accelerating until ou are on the freewa. Then ou turn the cruise control on and drive at a constant speed. When ou reach our exit, ou slow down as ou exit the freewa until ou stop at the stoplight. Temperature ( F) Altitude (ft) A.M. 8 A.M. P.M. P.M. 8 P.M. Time Speed 6,000,000 8,000,000 Rate cruising speeding up slowing down leaving station Time approaching station Time (min) Time Course 3 Lesson 3-

2 3- Functions A function describes the relationship between two variables called the input and the output. In a function, each input value has onl one output value. Function: x + c c output variable input variable x You can list input/output pairs in a table. x + Complete the table of input/output pairs for each function.. 3x. d 0r 3. 5 x Input x Input x 0 5 Output Output Input r Use the function rule 3x. Find each output.. when x when x. 3( ) + 3( ) + 3 To find output, substitute values for input x into the function equation. For x 0: ( 0) + 6 You can also show input/output pairs using function rules. Function rule: Find when x 0. Output d 60 x + ( 0) + 6 c c input output (0) + Input x 0 Output 9 6. when x when x 6. Course 3 Lesson 3-

3 3-3 Proportional Relationships A proportional relationship is a relationship between inputs and outputs in which the ratio of inputs and outputs is alwas the same. Gallons of Gas Cost ($) /3 /6 /3 3/9 /3 ; / /3 The ratios are all the same, so the relationship is proportional. Determine if the relationship is proportional... x a b m s Write the ratio of each input to its corresponding output. Then simplif. n t A pet store sells dog biscuits for $3 and 5 dog biscuits for $5. Is the relationship between the price of selling dog biscuits and 5 dog biscuits proportional? Explain. Course 3 Lesson 3-3

4 3- Linear Functions A function is linear if the relationship between the changes in variables is constant. x A function is not linear if the relationship between the changes in variables is not constant. x Graph each function. Determine if the function represented in the table is linear... x x Course 3 Lesson 3-

5 3- (continued) Linear Functions 3.. x x Course 3 Lesson 3-

6 3-5 Nonlinear Functions The graphs of nonlinear functions are not straight lines. A quadratic function is nonlinear. Its graph is a parabola x One wa to tell if a function is nonlinear is b looking at the functions greatest exponent. If it is or greater, the function in nonlinear. x 3 x 5 x 3 linear nonlinear nonlinear Identif each function as linear or nonlinear x 5. 8 d d d 0 8 x x Another wa to tell if a function is nonlinear is b using a table. If the ratios between the changes in variables in a table are not the same, then the function is nonlinear. The ratios,, and are not the same. The 6 0 table represents a nonlinear function... x 3 x 6. x x x Write a description of a situation that can be represented b a nonlinear function. Course 3 Lesson 3-5