Understanding Function Notation
Description: In this lesson, we will explore function notation, a key concept in Algebra I. Function notation provides a concise way to represent functions and their outputs. You will learn how to read and use function notation to solve problems.
Outline
- Introduction to Function Notation
- Examples of Function Notation
- Exercises and Solutions
- Homework
- Revision
Introduction to Function Notation
Function notation is used to represent functions in a compact way. If f(x) is a function, f is the name of the function and x is the input value. The function f(x) gives the output when x is substituted into the function.
Examples of Function Notation
Example 1:
Given the function f(x) = 2x + 3, find f(4).
Solution: Substitute x = 4 into the function:
f(4) = 2(4) + 3 = 8 + 3 = 11
Example 2:
For the function g(x) = x² - 5, calculate g(-2).
Solution: Substitute x = -2 into the function:
g(-2) = (-2)² - 5 = 4 - 5 = -1
Example 3:
Consider the function h(x) = 3x - 7. What is h(0)?
Solution: Substitute x = 0 into the function:
h(0) = 3(0) - 7 = -7
Example 4:
Find the output of the function f(x) = -x + 9 when x = 6.
Solution: Substitute x = 6 into the function:
f(6) = -6 + 9 = 3
Example 5:
Given p(x) = 4x - 1, determine p(3).
Solution: Substitute x = 3 into the function:
p(3) = 4(3) - 1 = 12 - 1 = 11
Example 6:
For the function q(x) = x/2 + 5, find q(8).
Solution: Substitute x = 8 into the function:
q(8) = 8/2 + 5 = 4 + 5 = 9
Exercises
Exercise 1:
Find f(5) if f(x) = x² + 2x.
Solution: Substitute x = 5:
f(5) = 5² + 2(5) = 25 + 10 = 35
Exercise 2:
Calculate g(-1) for g(x) = -3x + 4.
Solution: Substitute x = -1:
g(-1) = -3(-1) + 4 = 3 + 4 = 7
Exercise 3:
Determine h(2) if h(x) = 2x + 6.
Solution: Substitute x = 2:
h(2) = 2(2) + 6 = 4 + 6 = 10
Exercise 4:
What is f(-3) for f(x) = -x + 8?
Solution: Substitute x = -3:
f(-3) = -(-3) + 8 = 3 + 8 = 11
Exercise 5:
Find p(4) if p(x) = 3x - 7.
Solution: Substitute x = 4:
p(4) = 3(4) - 7 = 12 - 7 = 5
Exercise 6:
Determine q(0) for q(x) = x/3 + 2.
Solution: Substitute x = 0:
q(0) = 0/3 + 2 = 0 + 2 = 2
Exercise 7:
Given r(x) = 5x - 2, find r(-4).
Solution: Substitute x = -4:
r(-4) = 5(-4) - 2 = -20 - 2 = -22
Exercise 8:
Calculate s(6) for s(x) = x² + 3x.
Solution: Substitute x = 6:
s(6) = 6² + 3(6) = 36 + 18 = 54
Exercise 9:
What is t(-2) if t(x) = -2x + 5?
Solution: Substitute x = -2:
t(-2) = -2(-2) + 5 = 4 + 5 = 9
Exercise 10:
Find u(1) for u(x) = 7 - x.
Solution: Substitute x = 1:
u(1) = 7 - 1 = 6
Homework
- Complete Exercises 1-10 from the examples and practice problems provided.
- Create 5 additional functions and solve for different values of x.
- Write a brief explanation of why function notation is useful in algebra.
Revision
Review the following points to solidify your understanding of function notation:
- Function notation uses the format f(x) to represent functions and their outputs.
- Substitute the input value x into the function to find the output.
- Practice interpreting and solving function notation problems to gain confidence.
Learn More
Watch this video for a detailed explanation of function notation: Function Notation Explained
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