Lesson 2: Operations on Functions

What is the value of the function f(x) = 2x + 1 when x = 3?

What is the difference when subtracting g(x) from f(x) with f(x) = 2x³ - 3x + 4 and g(x) = 3x² + 2x - 6?

What is the value of the function g(x) = x² - 2x + 2 when x = 3?

What is the result of adding the functions f(x) = 2x³ - 3x + 4 and g(x) = 3x² + 2x - 6?

How do you combine like terms when evaluating the expression (2x³ - 3x + 4) + (3x² + 2x - 6)?

Function Evaluation

Evaluating functions involves substituting a given value for the variable.
For x = 3, the following evaluations are done:
- f(x) = 2x + 1 results in 7.
- g(x) = x² - 2x + 2 results in 5.
- f(x) = x² + 8x + 9 results in 27.

Addition of Functions (Sum)

Begin by substituting the variable values into the functions.
Rearrange the functions correctly, ensuring the signs are chosen appropriately.
Combine the variables, maintaining the correct exponents.
Collect like terms (LT) to simplify the result.

Subtraction of Functions (Difference)

Start by substituting values into the functions as needed.
Properly arrange the functions for clear subtraction.
Combine variables, keeping track of their exponents during the process.
Again, gather like terms (LT) together for the final expression.

Division of Functions

Consider the functions f(x) and g(x) defined as follows:
- f(x) = 2x³ - 3x + 4
- g(x) = 3x² + 2x - 6
For adding functions: (f + g)(x) combines both functions to yield:
- (2x³ - 3x + 4) + (3x² + 2x - 6) = 2x³ + 3x² - x - 2.
For subtracting functions: (f - g)(x) calculates the difference as:
- (2x³ - 3x + 4) - (3x² + 2x - 6) = 2x³ - 3x² - 5x + 10.

This quiz focuses on evaluating and performing operations on functions. You will substitute values, arrange equations, and combine like terms for addition, subtraction, and division of functions. Test your understanding of these key concepts in algebraic operations.