Calculator Lab
Coordinate Algebra: Unit 3
Name___________________ Date_________________ Period________
Lesson 10: Characteristics of Exponential Functions Notes
|Standard and Skills |
|F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs |
|showing key features given a verbal description of the relationship. |
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|SWBAT determine the domain and range of exponential functions. |
|SWBAT determine the asymptote of exponential functions |
|SWBAT determine the x and y intercepts of exponential functions |
|SWBAT determine the intervals of increase or decrease of exponential functions |
|SWBAT determine the rate of change between interval of exponential functions |
|SWBAT determine the end behavior of exponential functions |
Important Characteristics
• Asymptote: A line that a graph gets _____________________ and closer to, but never _____________ or touches
• X-Intercept : The point at which a line intersects the _______________ at __________
• Y-Intercept : The point at which a line intersects the _______________ at __________
• Increasing/Decreasing Behavior: Always move ______________ to ______________ !
If your finger is going ___________, the graph is _________________________
If your finger is going ___________, the graph is _________________________
If your finger doesn’t go up or down, then the graph is ____________________
• Domain: The set of all possible _______________________ (often the “x” variable)
• Range: The set of all possible ________________________(often the “y” variable)
• Rate of Change: The amount of ______________ (slope) at a part of a function. The change in ____________________ divided by the change in the __________________ values.
• End Behavior: The behavior of the graph of f(x) as x approaches _______________ or _______________ infinity. What is the function doing when x approaches infinity?
|Example 1: Find the characteristics for the exponential function. |
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|Guided Practice | |
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|Domain: __________________ |Domain: __________________ |
|Range: ___________________ |Range: ___________________ |
|X-intercept: _________ Y-intercept: ________ |X-intercept: _________ Y-intercept: ________ |
|Increasing or Decreasing |Increasing or Decreasing |
|Max or Min: ______________ |Max or Min: ______________ |
|Asymptote: _______________ |Asymptote: _______________ |
Independent Practice
1. A pendulum swings to 90% of its height on each swing and starts at a height of 80 cm. The height of the pendulum in centimeters, y, is recorded after x number of swings. Write the equation, and determine the key features of this function.
Equation: ___________________________
Domain: ____________________________
Range: _____________________________
Intercepts: ________________________
Max or Min: ________________________
Increasing or Decreasing: __________
Discrete or Continuous: _____________
2. Find the characteristics of each of the functions.
|x |[pic] |
|f(x) | |
| | |
|0 | |
|1 | |
| | |
|1 | |
|3 | |
| | |
|2 | |
|9 | |
| | |
|3 | |
|27 | |
| | |
| | |
|Equation: _______________ |Equation: _______________ |
|Domain: ________________ |Domain: ________________ |
|Range: _________________ |Range: _________________ |
|x-intercept: _____________ |x-intercept: _____________ |
|y-intercept: _____________ |y-intercept: _____________ |
|Increasing or Decreasing? |Increasing or Decreasing? |
|R.o.C. from x=1 to x=3 _________ |R.o.C. from x= -3 to x= -1 ________ |
3. The Honey Baked Ham store tracked how many hams they sold for Thanksgiving during the month of November. If they sold two hams on the first day and sold four-times as many each day, answer the following questions and graph the equation.
[pic]
4. A Dalmatian puppy is born with ten spots. If the number of spots increases each year according to the chart, answer the following questions.
|x |f(x) |
|0 |10 |
|1 |20 |
|2 |40 |
|3 |80 |
|4 |160 |
|5 |320 |
[pic]
5. Fall is upon us and the leaves are changing color. If two-thirds of the leaves on a tree are remaining after each week, use the graph below to answer the questions.
[pic]
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1. Domain: ______________
2. Range: _______________
3. Intercepts: ____________
4. Increasing or Decreasing ?
5. Max or Min?_____________
6. Asymptote: ______________
Hint: Each y-value is half of the previous y.
[pic]
a) Write the equation that represents how many spots the dalmation will have.
___________________________________
b) Calculate the average rate of change between years 1 and 3.
c) Calculate the average growth rate for the first five years [0, 5].
d) Which average growth rate is higher? Does this make sense?
a) Write an equation to represent the amount of leaves left on the tree.
___________________________________
b) Describe the domain and range of the function.
c) Calculate the average rate of change for the first seven weeks [0, 7].
d) How many weeks will it take for there to be no leaves left on the tree? *Hint: Use your table*
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