U1 L1.2: Evaluating Functions

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Created by
Ayen B.

Cards (55)

  • Learning Objectives: At the end of this lesson, you should be able to evaluate functions
  • Solution for Example 3
    To find š‘‡ 1 and š‘‰ āˆ’2, evaluate them separately and then subtract the results. š‘‡ 1 = 30, š‘‰ āˆ’2 = -8. Therefore, š‘‡ 1 āˆ’ š‘‰ āˆ’2 = 30 - (-8) = 38
  • Evaluating Functions
    To evaluate a function means to replace (or substitute) the variable in the function with a given number or expression. In simplifying a series of operations, we use the GEMDAS Rule
  • Solution for Example 1
    The expression š‘“ 2 means evaluating the function š‘“ š‘„ = 2š‘„ + 7 using š‘„ = 2. Replace š‘„ in the function with 2: š‘“ 2 = 2(2) + 7 = 4 + 7 = 11
  • Solution for Example 2
    The expression š‘” āˆ’3 means evaluating the function š‘” š‘„ = š‘„0 + 4š‘„ āˆ’ 5 using ļæ½ļæ½ = āˆ’3. Replace ļæ½ļæ½ with āˆ’3: š‘” āˆ’3 = āˆ’3(0) + 4(-3) - 5 = -8
  • Topics to revisit before starting the lesson
    • Evaluating algebraic expressions
    • Operations on algebraic expressions
    • Order of Operations (GEMDAS)
  • Therefore, š‘» šŸ āˆ’ š‘½ āˆ’ļæ½ļæ½ = šŸ‘šŸ”
  • Evaluating š‘‡ 1 āˆ’ š‘‰ āˆ’2
    š‘‡ 1 āˆ’ š‘‰ āˆ’2 = 30 āˆ’ āˆ’6 = 36
  • Example 4ā€Ø
    Evaluate š‘“ 2š‘„ + 1 if š‘“ š‘„ = 3ļæ½ļæ½ + 4
  • Evaluating Functions
    In the previous examples, we evaluated functions by replacing the variable in the function by a number. In some cases, we evaluate a function by replacing the variable in the function by some expressions
  • Evaluating š‘‡ 1
    1. š‘‡ š‘„ = 3 š‘„ + 9
    2. š‘‡ 1 = 3 1 + 9 = 3 10 = 30
  • If š‘» š’™ = šŸ ļæ½ļæ½ āˆ’ šŸ‘ and ļæ½ļæ½ ļæ½ļæ½ = ļæ½ļ潚’™ļæ½ļæ½ āˆ’ šŸ“š’™ + šŸ–, what is the value of š‘» šŸ āˆ’ š‘½ āˆ’šŸ ?
  • Evaluating š‘‰ āˆ’2
    1. š‘‰ š‘„ = 2š‘„0 + 4š‘„ āˆ’ 6
    2. š‘‰ āˆ’2 = 2 āˆ’2 0 + 4 āˆ’2 āˆ’ 6 = 2 4 āˆ’ 8 āˆ’ 6 = 8 āˆ’ 8 āˆ’ 6 = āˆ’6
  • Solution for Example 5
    To solve for š‘” š‘„ + ā„Ž, we need to replace the variable š‘„ in the function š‘” š‘„ = š‘„0 + 4š‘„ āˆ’ 6 with the expression š‘„ + ā„Ž. š‘” š‘„ + ā„Ž = š‘„ + ā„Ž 0 + 4 š‘„ + ā„Ž āˆ’ 6
  • Evaluating Functions
    In order to find the value š‘‡ 1 āˆ’ š‘‰ āˆ’2, we need to evaluate ļæ½ļæ½ 1 and ļæ½ļæ½ āˆ’2 separately, and then subtract the results
  • Example 5
    Given that š‘” š‘„ = š‘„0 + 4š‘„ āˆ’ 6, solve for š‘” š‘„ + ā„Ž
  • Solution for Example 4
    The expression š‘“ 2š‘„ + 1 means that we are going to replace the variable š‘„ in the function š‘“ š‘„ = 3š‘„ + 4 with 2š‘„ + 1. ļæ½ļæ½ 2ļæ½ļæ½ + 1 = 3 2š‘„ + 1 + 4 = 6š‘„ + 3 + 4 = 6š‘„ + 7
  • The Wealth of Nations was written
    1776
  • Given that ļæ½ļæ½ š’™ = š’™ļæ½ļæ½ āˆ’ ļæ½ļ潚’™ + šŸ—, solve for š’• š’™ + š’‰
  • To solve for š‘” š‘„ + ā„Ž, we need to replace the variable š‘„ in the function š‘” š‘„ = š‘„0 + 4š‘„ āˆ’ 6 with the expression š‘„ + ā„Ž
  • Evaluating š‘“ 2
    1. Identify the location of š‘„ = 2
    2. Locate where š‘„ = 2 lies in the piecewise function
    3. Identify the value of š‘“ 2 by using the expression 5š‘„0 + 4
  • Solving for š‘” š‘„ + ā„Ž
    1. Replace š‘„ in š‘” š‘„ = š‘„0 + 4š‘„ āˆ’ 6 with š‘„ + ā„Ž
    2. Simplify the algebraic expression to get the result š‘” š‘„ + ā„Ž = š‘„0 + 2ā„Žš‘„ + ā„Ž0 + 4š‘„ + 4ā„Ž āˆ’ 6 = š‘„šŸ + šŸā„Žš‘„ + ā„ŽšŸ + šŸ’š‘„ + šŸ’ā„Ž āˆ’ šŸ”
  • Evaluating š‘“ 0
    Identify the location of š‘„ = 0 in the piecewise function
  • In the next examples, we are going to learn how to evaluate piecewise functions
  • Given the piecewise function š‘“ š‘„ = E š‘„F + 1, if š‘„ ā‰¤ 1, evaluate š‘“ 2 and š‘“ 0
  • Try This!
  • Given the piecewise function š‘† š‘„ā€Ø
    1. Evaluate the following:
    2. š‘† 3
    3. š‘† āˆ’4
    4. š‘† 6
  • Evaluating Functions
  • Solution
  • Evaluating š‘†(3)
    1. Locate š‘„ = 3 in the piecewise function
    2. Use the expression 8 āˆ’ 3ļæ½ļæ½ āˆ’ 4ļæ½ļæ½0 to evaluate š‘† 3 = 8 āˆ’ 3 3 āˆ’ 4 3 0 = 8 āˆ’ 3 3 āˆ’ 4 9 = 8 āˆ’ 9 āˆ’ 36 = āˆ’37
  • Given the piecewise function š‘† š‘„
    1. Evaluate the following:
    2. ļæ½ļæ½ āˆ’šŸ‘
    3. š‘† šŸ
  • Evaluating š‘†(6)
    Locate š‘„ = 6 in the piecewise function
  • Evaluating š‘“ 0
    1. Identify the location of š‘„ = 0 in the piecewise function
    2. Identify the value of š‘“ 0 by using the expression š‘„F + 1
    3. Calculate š‘“ 0 = 0 F + 1 = 0 + 1 = 1
  • Given the piecewise function
  • De La Salle Medical and Health Sciences Institute - Special Health Sciences Senior High School
  • Evaluating š‘†(āˆ’4)ā€Ø
    1. Locate š‘„ = āˆ’4 in the piecewise function
    2. Use the expression āˆ’2 2ļæ½ļæ½ āˆ’ 4 to evaluate š‘† āˆ’4 = āˆ’2 2 āˆ’4 āˆ’ 4 = āˆ’2 āˆ’8 āˆ’ 4 = āˆ’2 āˆ’12 = 24
  • Example 7:
  • Evaluate the following:
    1. š‘† 2
    2. š‘† -6
    3. š‘† 9
  • The expression š‘“ 1 means that we are looking for the š‘¦-value that corresponds to š‘„ = 1
  • Evaluating Functionsā€Ø
    We will learn how to evaluate functions based on their graphs