Function Operations: Adding and Subtracting Functions

Algebra 2 Grades High School 2:47 Video
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Lesson Description

Learn how to add and subtract functions algebraically, including proper use of parentheses and substitution.

Video Resource

Add Subtract Functions Algebra

Kevinmathscience

Duration: 2:47
Watch on YouTube

Key Concepts

  • Function Notation
  • Combining Like Terms
  • Substitution
  • Polynomial Arithmetic

Learning Objectives

  • Students will be able to add two or more functions together.
  • Students will be able to subtract one function from another, paying attention to the distribution of the negative sign.
  • Students will be able to evaluate the resulting function at a given value.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of functions and function notation. Briefly discuss polynomial expressions. Introduce the idea that functions can be added and subtracted just like algebraic expressions.
  • Adding Functions (10 mins)
    Explain that to add functions, we combine like terms. Go through an example, such as the one in the video (G + H), where G(t) = 4t - 5 and H(t) = -2t - t^2. Emphasize the importance of writing the resulting polynomial in standard form.
  • Subtracting Functions (15 mins)
    Explain that subtracting functions requires distributing the negative sign. Using the video example (H - G), where H(t) = 3t - 2 and G(t) = t^3 - 1, show how the negative sign affects each term in the second function. Stress the necessity of using parentheses to ensure the negative sign is properly distributed. Simplify the resulting expression by combining like terms.
  • Evaluating Combined Functions (15 mins)
    Explain that after adding or subtracting functions, the result can be evaluated at a specific x-value. Use the example from the video where H(x) = 3x - 4 and G(x) = x - 5 and we need to find H(x) + G(x) evaluated at x = -4. First find H(x)+G(x) = 4x -9. Then substitute -4 for x. Work through the arithmetic carefully, explaining each step.
  • Practice Problems (15 mins)
    Provide students with practice problems that require them to add, subtract, and evaluate functions. Include problems that require distributing a negative sign and combining like terms. Encourage students to work independently or in pairs.
  • Wrap-up (5 mins)
    Review the main concepts of the lesson. Answer any remaining questions. Preview the next lesson on function composition.

Interactive Exercises

  • Function Match
    Provide students with a list of function expressions and a list of their simplified forms. Students must match the original expressions to their simplified forms after addition or subtraction.
  • Error Analysis
    Present students with worked-out problems containing common errors (e.g., incorrect distribution of the negative sign). Students must identify and correct the errors.

Discussion Questions

  • Why is it important to use parentheses when subtracting functions?
  • When adding or subtracting functions, how do you know which terms can be combined?
  • What does it mean to evaluate a function at a specific value?

Skills Developed

  • Algebraic manipulation
  • Attention to detail
  • Problem-solving
  • Critical thinking

Multiple Choice Questions

Question 1:

If f(x) = 2x + 3 and g(x) = x - 1, what is (f + g)(x)?

Correct Answer: 3x + 2

Question 2:

If f(x) = x^2 - 4 and g(x) = 2x + 1, what is (f - g)(x)?

Correct Answer: x^2 - 2x - 5

Question 3:

Given f(x) = 3x - 2 and g(x) = x + 5, what is (f + g)(2)?

Correct Answer: 11

Question 4:

If f(x) = x^2 + 1 and g(x) = x - 3, what is (f - g)(0)?

Correct Answer: 4

Question 5:

Let f(x) = 4x and g(x) = x^2 - x. What is (g - f)(x)?

Correct Answer: x^2 - 5x

Question 6:

If h(x) = -x^3 + 2x and k(x) = 5x, then what is (h+k)(x)?

Correct Answer: -x^3 + 7x

Question 7:

Given p(x) = 2x^2 - 1 and q(x) = -x^2 + x, then what is (p-q)(1)?

Correct Answer: 0

Question 8:

If f(x) = sqrt(x) and g(x) = 2sqrt(x), what is f(x) + g(x)?

Correct Answer: 3sqrt(x)

Question 9:

Given f(x) = 5/x and g(x) = 2/x, what is (f - g)(x)?

Correct Answer: 3/x

Question 10:

If a(x) = x^2 + x + 1 and b(x) = x - 1, then what is (a+b)(-1)?

Correct Answer: 0

Fill in the Blank Questions

Question 1:

When subtracting functions, it is important to ____________ the negative sign to all terms in the second function.

Correct Answer: distribute

Question 2:

To add functions, we combine ___________ __________.

Correct Answer: like terms

Question 3:

If f(x) = x + 2 and g(x) = 2x - 1, then (f + g)(x) = __________.

Correct Answer: 3x + 1

Question 4:

If h(x) = x^2 and k(x) = x + 3, then (h - k)(x) = __________.

Correct Answer: x^2 - x - 3

Question 5:

Given f(x) = 5x and g(x) = x - 4, then (f + g)(1) = __________.

Correct Answer: 2

Question 6:

If p(x) = 2x + 1 and q(x) = -x + 3, then (p - q)(0) = __________.

Correct Answer: -2

Question 7:

Function addition and subtraction is also known as ____________ arithmetic.

Correct Answer: polynomial

Question 8:

If f(x) = 2/x and g(x) = 5/x, then f(x) + g(x) = __________.

Correct Answer: 7/x

Question 9:

If f(x) = x^2 and g(x) = x, then (g-f)(x) = _________.

Correct Answer: -x^2+x

Question 10:

If a(x) = x+2 and b(x) = x^2, then (a+b)(2) = __________.

Correct Answer: 6

Educational Standards

A2.A.2.2:Add, subtract, multiply, divide, and simplify polynomial expressions. A2.F.1.1:Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain.

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