Understanding Fractions and Functional Notation

This lesson covers fractional parts of numbers and functional notation. It begins with solving problems involving fractional parts, explaining key terms like 'of' and 'is' in algebraic expressions. The lesson then transitions to functional notation, demonstrating how to evaluate functions by substituting values for variables. Through examples, students learn to solve equations and understand the importance of order of operations in function evaluation.

What operation does the word 'of' indicate in the context of fractional parts of numbers?

• Addition

• Division

• Subtraction

• Multiplication

If three-fourths of a number is 69, what is the number?

• 92

• 69

• 23

• 46

How do you convert a mixed number to an improper fraction?

• Add the whole number to the fraction

• Multiply the whole number by the denominator and add the numerator

• Subtract the fraction from the whole number

• Divide the numerator by the denominator

What is two and one-half of 240?

• 480

• 600

• 360

• 120

What is the first step in evaluating an expression using functional notation?

• Add all terms

• Substitute the given value for the variable

• Divide all terms

• Multiply all terms

What is the result of evaluating the expression 2(x^2 - 3x) when x = 2?

• 8

• 0

• -4

• 4

In functional notation, what does f(2) represent?

• The function evaluated at x = 0

• The function evaluated at x = -2

• The function evaluated at x = 2

• The function evaluated at x = 1

What is the value of g(-2) for the function g(x) = x^2(2x - 1)?

• -20

• 20

• -10

• 10

When using functional notation, what does it mean to 'evaluate' a function?

• To find the derivative

• To integrate the function

• To substitute a specific value for the variable

• To graph the function

What is the purpose of using functional notation in mathematics?

• To perform arithmetic operations

• To evaluate functions at specific values

• To solve equations

• To simplify expressions