Graphing Characteristics Warm Up 1. Complete the following table by writing the independent and dependent variables. Independent Variable Dependent Variable Ex: Number of hours you study for a test Your test score Number of gallons in your gas tank Your IQ (intelligence quotient) The number of calories you eat each day Your level of happiness 2. A local youth group is planning a trip to a local amusement park. They are taking their church bus, which holds 32 people. It will cost $25 for parking and tickets to enter the park are $22.50 per person. The equation that models this situation is: c(n) = 22.5n + 25, where c represents the cost for the group to go the park and n represents the number of people who go on this excursion. Independent Variable: Domain: Dependent Variable: Range: 3. Ms. Hahn found $2.70 in her car in only quarters and dimes. If x represents quarters and y represents dimes and y is a function of x, find the domain of the function. 4. You just found $4.40 in the couch cushions in only quarters and dimes. If x represents quarters and y represents dimes and y is a function of x, find the range of the function. Graph Vocab Determine the characteristics of the following graph and provide a definition. Characteristic y-‐intercept From the Graph Above Definition x-‐intercept(s) Absolute Maximum Absolute Minimum Relative Maximum Relative Minimum Domain Range Intervals of Increasing Intervals of Decreasing Try one yourself: 1. y-‐intercept 2. x-‐intercept(s) 3. Maximums (relative or absolute?) 4. Minimums (relative or absolute?) 5. Domain 6. Range 7. Intervals of increasing 8. Intervals of decreasing Design Your Own Rollercoaster! Using today’s vocab, you and an assigned partner will design a rollercoaster. You must include: -‐ Name of rollercoaster -‐ Labeled axes and scale (graph paper will be provided). (Let the x-‐axis represent the horizontal distance from the starting platform and let the y-‐axis represent the vertical distance off the ground.) -‐ Y-‐intercept -‐ X-‐intercepts -‐ Maximums and minimums, labeled as relative or absolute. -‐ Domain and range (be realistic!) -‐ Intervals of increasing and decreasing -‐ Be creative – your rollercoaster can go underground, can go in loops, etc. Answer the following questions: 1.) Does your rollercoaster represent a function? Why or why not? 2.) What do the x-‐intercepts represent for the rollercoaster? 3.) What does the y-‐intercept represent for the rollercoaster? Practice 1. a) y-‐intercept b) x-‐intercept(s) c) Maximums (relative or absolute?) d) Minimums (relative or absolute?) e) Domain f) Range g) Intervals of increasing h) Intervals of decreasing 2. a) y-‐intercept b) x-‐intercept(s) c) Maximums (relative or absolute?) d) Minimums (relative or absolute?) e) Domain f) Range g) Intervals of increasing h) Intervals of decreasing
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