Calculator Lab - Weebly



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. |

| |

| |

|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. |

| |

| |

|Guided Practice | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

|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]

-----------------------

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*

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download