holt mcdougal algebra 2 6-1 multiple representations of functions 6-1 multiple representations of...
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Holt McDougal Algebra 2
6-1 Multiple Representations of Functions6-1 Multiple Representations of Functions
Holt Algebra 2
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Holt McDougal Algebra 2
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
• Express a function using function notation.• Evaluate values in the domain of a function.• Interpret functions in function notation based on context.
I can:
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
An amusement park manager estimates daily profits by multiplying the number of tickets sold by 20. This verbal description is useful, but other representations of the function may be more useful.
These different representations can help the manager set, compare, and predict prices.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Because each representation of a function (words, equation, table, or graph) describes the same relationship, you can often use any representation to generate the others.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
A function is a special type of relation that pairs each domain value with exactly one range value.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
The domain of a relation is the set of first coordinates (or x-values) of the ordered pairs. The range of a relation is the set of second coordinates (or y-values) of the ordered pairs. The domain of the track meet scoring system is {1, 2, 3, 4}. The range is {5, 3, 2, 1}.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Recreation Application
Janet is rowing across an 80-meter-wide river at a rate of 3 meters per second. Create a table, an equation, and a graph of the distance that Janet has remaining before she reaches the other side. When will Janet reach the shore?
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Continued
Step 1 Create a table.
Let t be the time in seconds and d be Janet’s distance, in meters, from reaching the shore.
Janet begins at a distance of 80 meters, and the distance decreases by 3 meters each second.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Continued
Step 2 Write an equation.
is equal to minus Distance 80 3 meters per second.
d = 80 – 3t
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Example 2 Continued
Step 3 Find the intercepts and graph the equation.
d-intercept:80
Solve for t when d = 0
0 = 80 – 3t
t = = 26–80–3
2 3
d = 80 – 3t
t-intercept: 26 2 3
Janet will reach the shore after seconds.26 2 3
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Evaluating Functions:
• On my websitehttps://
www.tranlordylordylordmath.weebly.com
• Click on Evaluating Function PracticeView the 3 videos examples 1-3• Then click on Understanding Function
Notation for practice
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Practice Interpretation and Evaluation in Real World Applications•Click on Interpreting Domain and Range Worksheet
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
•How do we know whether a given function is:
1. Linear2. Quadratic3. Exponential• This is Math 1/Algebra 1 Review
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Example 3: Using Multiple Representations to Solve Problems
A hotel manager knows that the number of rooms that guests will rent depends on the price. The hotel’s revenue depends on both the price and the number of rooms rented. The table shows the hotel’s average nightly revenue based on room price. Use a graph and an equation to find the price that the manager should charge in order to maximize his revenue.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Example 3A Continued
The data do not appear to be linear, so check finite differences.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Example 3A Continued
Revenues 21,000 22,400, 23,400 24,000
First differences 1,400 1,000 600
Second differences 400 400
Because the second differences are constant, a quadratic model is appropriate. Use a graphing calculator to perform a quadratic regression on the data.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Example 3B: Using Multiple Representations to Solve Problems
An investor buys a property for $100,000. Experts expect the property to increase in value by about 6% per year. Use a table, a graph and an equation to predict the number of years it will take for the property to be worth more than $150,000.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
Example 3B Continued
Make a table for the property. Because you are interested in the value of the property, make a graph, by using years t as the independent variable and value as the dependent variable.
Holt McDougal Algebra 2
6-1 Multiple Representations of Functions
The data appears to be exponential, so check for a common ratio.
r1 = = = 1.06 y1
y0
106,000100,000
r2 = = = 1.06 y2
y1
112,360106,000
r3 = = ≈ 1.06 y3
y2
119,102112,360
r4 = = ≈ 1.06 y4
y3
126,248119,102
Because there is a common ratio, an exponential model is appropriate. Use a graphing calculator to perform an exponential regression on the data.
Example 3B Continued