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Understanding Functions and Relations: Equations and Notation

This resource covers solving equations and understanding functions and relations in algebra. It includes step-by-step examples for solving linear equations and making sense of function notation, illustrating how to evaluate functions for specific values. Key concepts include distinguishing between functions and non-functions, using function notation (f(x)), and graphical representation of linear functions. Students will learn to apply the vertical line test to identify functions and develop skills for evaluating and graphing linear equations effectively.

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Understanding Functions and Relations: Equations and Notation

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  1. WARM UP 3 Solve the equation 4x + 8 = 24 3x – 5x = -12 3x + 9 = 9x - 7

  2. WARM UP 2 Solve the equation x + 6 = 14 9 – y = 4 4x + 5y =15

  3. WARM UP 1 Solve the equation x + 6 = 14 9 – y = 4 4x + 5y =15

  4. WARM UP 0 Solve the equation x + 6 = 14 9 – y = 4 4x + 5y =15

  5. 4.8 Functions and Relations Today’s Schedule: Lesson 4.8 Powerpoint In class assignment/homework Exit Slip GOAL: Decide whether a relation is a function and use function notation. KEY WORDS: relation, function, vertical line test, function notation, linear function.

  6. 4.8 Functions and Relations FUNCTION NOTATION When a function is defined by an equation, it is often convenient to name the function. Just as x is commonly used as a variable, the letter f is commonly used to name a function. To write a function using FUNCTION NOTATION, you use f(x) in place of y. x-y notation: y = 3x + 2 function notation: f(x) = 3x + 2

  7. 4.8 Functions and Relations SOLUTION You can evaluate a function for a given value by substituting the iven value for the variable and simplifying. EXAMPLE 3: Evaluate a Function Evaluatef(x) = 2x -3 when x = -2 • Write the original function. • Substitute -2 for x. • Simplify.

  8. 4.8 Functions and Relations a. Evaluate f(x) = 4x + 5 when x = 2 b. Evaluate g(x) = x2when x = 3 CHECKPOINT: Evaluate a Function

  9. 4.8 Functions and Relations LINEAR FUNCTION A function is called a linear function if it is of the form f(x) = mx + b. For instance, the function in Example 3 part a is linear. But, the function in Example 3 part b is not linear. To graph a linear function, rewrite the function using x-y notation.

  10. 4.8 Functions and Relations SOLUTION • Rewrite the function in x-y notation. • Find the slope and the y-intercept • Use slope to find a second point • Draw a line through the two points EXAMPLE 4: Graph a Linear Function Graphf(x) = -2x + 3

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