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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. Based on the tables, which relations are functions and which are not? Give a reason for your answer. Table 1 Table 2 Table 3 Table 4 Input Output Input Output Input Output Input Output -2 -3 4 -2 -2 0.44 -2 -3 -1 -1 1 -1 -1 0.67 -1 -5 0 1 0 0 0 1 1 -1 1 3 1 1 1 1.5 1 -3 2 5 4 2 2 2.25 2 -10 3 7 9 3 3 3.37 3 -2 4 9 16 4 4 5.06 3 -8 Each algebraic statement below represents a relation. Based on the equations, which relations are functions and which are not? Give reasons for your answer. Statement 1 y 1 2x Statement 2 y2 x Statement 3 y 1.5x Statement 4 2 y 1 x 3 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 1 3x y=a+bx form Intercept form y 0.5x 2 y=mx +b form Slope intercept form y 3 x 4 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. 2x 3y 6 y 5 2(x 8) ax +by = c form Standard form y=y1 +b(x-x1) form Point-slope form y 7 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 9 x= k form Vertical line 2x 4y 12 Boundary line, in standard form, of an inequality