word problems function notes absent copy thurs fri 4 11 12 n.
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Function and its rulesA function is a set of ordered pairs (x,y) so that each x value we pick corresponds to exactly one y value after we solve.Ex: y = 2x + 3 (2,7) 7 = 2(2) + 3 7 = 4 + 3 7 = 7 y = 2x + 9Function ruleoutput = y input = x

example 1
Example 1
  • A taxi driver charges a flat rate of 2 dollars to ride in a cab. He also charges 1 dollars for every mile that he has to drive. Write an equation that represents a person that travels from 1 to 3 miles in a cab and how much it costs for each ride. Hint: y = total cost and x = the number of miles the taxi drove.

y = 1x + 2

  • How do we write the equation of a line in slope intercept form?
  • Y = mx + b
  • What is the constant (b) that never changes in the word problem?
  • b = 2
  • What is the slope (m) in this word problem.
  • m = 1
  • What input (X) do we have to substitute in to the linear equation in order to find the total cost (output, Y) for each ride?
  • 1 to 3 can be put in for the input.
graph example 1
Graph example 1
  • Show the work from example 1 Below.

1. y = 1(1) + 2

y = 1 + 2

y = 3 (1,3)

  • Y = 1(2) + 2

y = 2 + 2

y = 4 ( 2,4)

  • Y = 1(3) + 2

y = 3 + 2

y = 5 ( 3,5)

example 2
Example 2
  • Shasta pays $1 for a can of dog food each day. She also pays $2 for each cookie she buys. Write an equation that represents Shasta buying 1 to 3 cookies and how much is her total treat fee.

y = 2x + 1

  • How do we write the equation of a line in slope intercept form?
  • Y = mx + b
  • What is the constant (b) that never changes in the word problem?
  • b = 1
  • What is the slope (m) in this word problem.
  • m = 2
  • What input (X) do we have to substitute in to the linear equation in order to find the total cost (output, Y) for each ride?
  • 1 to 3 cookies is the input
graph from example 2
Graph from Example 2
  • Show the work from example 2 Below.
  • 1. y = 2(1) + 1

y = 2 + 1

y = 3 (1,3)

  • 2. y = 2(2) + 1

y = 4 + 1

y = 5 (2,5)

  • 3. y = 2(3) + 1

y = 6 + 1

y = 7 (3,7)