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Holt McDougal Algebra 2
Multiple Representations of FunctionsMultiple Representations of Functions
Holt Algebra 2Holt McDougal Algebra 2
• How do we translate between the various representations of functions?
• How do we solve problems by using the various representations of functions?
Holt McDougal Algebra 2
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
Multiple Representations of Functions
Recreation Application1. 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?
is equal to minus Distance 80 3 meters per second.
td 380
Holt McDougal Algebra 2
Multiple Representations of Functions
Recreation Application1. 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?
td 380 t3
0t3t380
3 367.26t sec
Holt McDougal Algebra 2
Multiple Representations of Functions
Recreation Application2. The table shows the height, in feet, of an arrow in relation to its
horizontal distance from the archer. Create a graph, an equation, and a verbal description to represent the height of the arrow with relation to its horizontal distance from the archer.
Step 1 Use the table to check finite differences.
First differences 53.25 30.75 8.25 –14.3 –37Second differences –22.5 –22.5 –22.55 –22.7
Since second differences are close to constant, use the quadratic regression feature to write an equation.
Holt McDougal Algebra 2
Multiple Representations of Functions
Recreation Application2. The table shows the height, in feet, of an arrow in relation to its
horizontal distance from the archer. Create a graph, an equation, and a verbal description to represent the height of the arrow with relation to its horizontal distance from the archer.
Step 2 Write an equation. Use the quadratic regression feature.
y = –0.002x2 + 0.86x + 6.52
Holt McDougal Algebra 2
Multiple Representations of Functions
Recreation Application2. The table shows the height, in feet, of an arrow in relation to its
horizontal distance from the archer. Create a graph, an equation, and a verbal description to represent the height of the arrow with relation to its horizontal distance from the archer.
Step 3 Graph the equation. 100
50000
The archer shoots the arrow from a height of 6.55 ft. It travels horizontally about 220 ft to its peak height of about 99 ft, and then it lands on the ground about 500 ft away.
Holt McDougal Algebra 2
Multiple Representations of Functions
Holt McDougal Algebra 2
Multiple Representations of Functions
The point-slope form of the equation of a line is y – y1 = m(x – x1), where m is the slope and (x1, y1) is a point on the line. (Lesson 2-4)
Remember!
First differences are constant in linear functions. Second differences are constant in quadratic functions. (Lesson 5-9)
Remember!
Holt McDougal Algebra 2
Multiple Representations of Functions
Using Multiple Representations to Solve Problems3. 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.
The data do not appear to be linear, so check finite differences.
Holt McDougal Algebra 2
Multiple Representations of Functions
Using Multiple Representations to Solve Problems3. 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.
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
Multiple Representations of Functions
Using Multiple Representations to Solve Problems3. 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.
xxy 4402 2 Use the Maximum Feature to locate the maximum.
Occurs when x = 110The manager should charge $110 a night per room.
Holt McDougal Algebra 2
Multiple Representations of Functions
Lesson 12.1 Practice B
