Function Evaluation: Mastering Substitution in Algebra

Algebra 2 Grades High School 5:32 Video
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Lesson Description

Learn how to evaluate functions by substituting given values, a fundamental skill in Algebra 2. This lesson covers the basics and progressively tackles more complex examples, reinforcing understanding and accuracy.

Video Resource

Evaluating Functions Algebra

Kevinmathscience

Duration: 5:32
Watch on YouTube

Key Concepts

  • Function notation
  • Substitution
  • Order of operations
  • Absolute value

Learning Objectives

  • Students will be able to correctly substitute given values into functions.
  • Students will be able to evaluate functions involving absolute values.
  • Students will be able to apply the correct order of operations when evaluating functions.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of a function and function notation (e.g., f(x)). Briefly discuss how 'f(x)' represents the output of a function for a given input 'x'. Emphasize that evaluating a function means finding the output for a specific input.
  • Video Presentation (10 mins)
    Play the Kevinmathscience video 'Evaluating Functions Algebra'. Instruct students to pay close attention to the examples and the process of substitution.
  • Guided Practice (15 mins)
    Work through the examples from the video step-by-step on the board, emphasizing the importance of using brackets when substituting. Explain common mistakes, like handling negative signs correctly. Address any questions from students.
  • Independent Practice (15 mins)
    Provide students with additional practice problems of varying difficulty levels. Include functions with absolute values, negative signs, and exponents. Circulate to provide assistance and monitor understanding.
  • Wrap-up and Assessment (5 mins)
    Summarize the key concepts of function evaluation. Administer the multiple-choice and fill-in-the-blank quizzes to assess student learning.

Interactive Exercises

  • Substitution Challenge
    Present students with a series of functions and input values. Students compete (individually or in teams) to correctly evaluate the functions as quickly as possible.

Discussion Questions

  • Why is it important to use brackets when substituting values into a function?
  • How does the order of operations affect the evaluation of a function?
  • What are some common mistakes to avoid when evaluating functions with negative signs or absolute values?

Skills Developed

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

Multiple Choice Questions

Question 1:

What does f(3) mean if f(x) = 2x + 1?

Correct Answer: 2 * 3 + 1

Question 2:

If g(x) = x^2 - 4, what is g(-2)?

Correct Answer: 0

Question 3:

Given h(x) = |x - 5|, what is h(2)?

Correct Answer: 3

Question 4:

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

Correct Answer: -4

Question 5:

For the function k(x) = 5x - 7, find k(4).

Correct Answer: 13

Question 6:

If m(x) = |2x + 1|, what is m(-3)?

Correct Answer: 5

Question 7:

Given p(x) = x^3 - 2x + 1, what is p(0)?

Correct Answer: 1

Question 8:

If q(x) = -3x + 5, what is q(2)?

Correct Answer: -1

Question 9:

For the function r(x) = |x| + x, what is r(-4)?

Correct Answer: 8

Question 10:

If s(x) = (x + 1)/(x - 1), what is s(2)?

Correct Answer: 3

Fill in the Blank Questions

Question 1:

If f(x) = 4x - 3, then f(2) = _______.

Correct Answer: 5

Question 2:

If g(x) = x^2 + 1, then g(-1) = _______.

Correct Answer: 2

Question 3:

If h(x) = |x + 2|, then h(-5) = _______.

Correct Answer: 3

Question 4:

If k(x) = -2x + 6, then k(0) = _______.

Correct Answer: 6

Question 5:

If m(x) = 3|x|, then m(-2) = _______.

Correct Answer: 6

Question 6:

If p(x) = x^3, then p(-1) = _______.

Correct Answer: -1

Question 7:

If q(x) = 5 - x, then q(7) = _______.

Correct Answer: -2

Question 8:

If r(x) = |x| - x, then r(-3) = _______.

Correct Answer: 6

Question 9:

If s(x) = (x - 2)/(x + 1), then s(3) = _______.

Correct Answer: 1/4

Question 10:

If t(x) = -x^2 - 1, then t(2) = _______.

Correct Answer: -5

Educational Standards

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.

Teaching Materials

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