- 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 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.. What was the airplane s altitude for most of the flight?,000 ft. How long did it take the airplane to reach an altitude of,000 ft? 0 min. The third segment in the graph is not as steep as the first segment. What does this mean? The airplane ascends faster than it descends. 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) 70 60 50 0 0 0 0 0 A.M. A.M. P.M. P.M. P.M. Time Speed 6,000,000,000,000 Rate cruising speeding up slowing down leaving station Time approaching station 0 0 0 0 0 50 60 Time (min) Time Course Lesson -
- 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 + Input x 0 5 Output 6 6 0 6 Complete the table of input/output pairs for each function.. x. d 0r. 5 x Input x 5 7 9 Output 5 7 Input r Use the function rule x. Find each output.. when x 0. 5. when x. ( 0 ) + ( ) + 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 0 0 60 60 x + ( 0) + 6 c c input output (0) + Input x 0 Output 5 9 6. when x 5. 7. when x 6. 6 7 Course Lesson -
- 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 ($) 6 9 Yes No / /6 / /9 / ; / / The ratios are all the same, so the relationship is proportional. Determine if the relationship is proportional... x.. a b 0 6 9 6 5 m s Write the ratio of each input to its corresponding output. Then simplif. Yes No n 6 5 0 6 t 0 0 60 0 00 50 0 0 5. A pet store sells dog biscuits for $ and 5 dog biscuits for $5. Is the relationship between the price of selling dog biscuits and 5 dog biscuits proportional? Explain. No. The ratio of to is not the same as the ratio of to 5. Course Lesson -
- Linear Functions A function is if the relationship between the changes in variables is constant. x 5 6 9 5 A function is not if the relationship between the changes in variables is not constant. x 6 6 0 6 6 6 6 5 Graph each function. Determine if the function represented in the table is... x 5 0 7 x 7 7 non 5 5 6 5 Course Lesson -
- (continued) Linear Functions.. x 5 7 Check students graphs. x 5 7 0 non Course Lesson -
-5 Non Functions The graphs of non functions are not straight lines. A quadratic function is non. Its graph is a parabola. 0 x One wa to tell if a function is non is b looking at the functions greatest exponent. If it is or greater, the function in non. x x 5 x non non Identif each function as or non... x 5. d d d 0 x x 6 6 66 Another wa to tell if a function is non is b using a table. If the ratios between the changes in variables in a table are not the same, then the function is non. The ratios,, and are not the same. The 6 0 table represents a non function... x x 6. x 7 7 0 x 6 0 non non x 0 non 7. Write a description of a situation that can be represented b a non function. Check students answers. Course Lesson -5