Lesson 7-2 Functions and Graphs To learn the definition of function To learn about properties and geometric representations of functions. Lesson 7-2

You can write rules to show the relationship between input and output values using a Table Equation Graph Diagram

Each table represents a relation Each table represents a relation. Based on the tables, which relations are functions and which are not? Give a reason for your answer. Table 1 Input Output -2 -3 -1 1 3 2 5 7 4 9 Table 2 Input Output 4 -2 1 -1 2 9 3 16 Table 3 Input Output -2 0.44 -1 0.67 1 1.5 2 2.25 3 3.37 4 5.06 Table 4 Input Output -2 -3 -1 -5 1 2 -10 3 -8

Each algebraic statement below represents a relation Each algebraic statement below represents a relation. Based on the equations, which relations are functions and which are not? Give reasons for your answer.

Each graph below represents a relation Each graph below represents a relation. Move a vertical line, such as the edge of a ruler, from side to side on the graph. Based on the graph and your vertical line, which relations are functions and which are not? Give reasons for your answer. Graph 1 Graph 2 Graph 3 Graph 4 Use your results to write a rule explaining how you can determine whether a relation is a function based on its graph.

A function is a relation between input and output values. Each input has exactly one output. The vertical line test helps you determine if a relation is a function. If all possible vertical lines cross the graph once or not at all, then the graph represents a function.

Name the form of each linear equation or inequality, and use a graph to explain why it is or is not a function. y=a+bx form Intercept form y=mx +b form Slope intercept form y=kx form Direct variation All three equations and graphs represent functions because every x input corresponds with exactly one y output.

Name the form of each linear equation or inequality, and use a graph to explain why it is or is not a function. ax +by = c form Standard form y=y1 +b(x-x1) form Point-slope form y=k form Horizontal line

Name the form of each linear equation or inequality, and use a graph to explain why it is or is not a function. x= k form Vertical line Boundary line, in standard form, of an inequality