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Transcript
Find examples that support or refute your classmates’ answers to the discussion question. Provide additional similarities and differences between functions and linear equations. Challenge your classmates by providing more intricate examples of nonlinear functions for them to solve To test a function you can use the vertical line test, If the vertical line crosses the line in 2 or more points, then the equation is not a function . Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate. Student1: What similarities and differences do you see between functions and linear equations studied in Ch. 3? Functions are often described by graphs, whether or not an equation is given. To use a graph in an application, we note that each point on the graph represents a pair of values. As in chapter three called ordered pairs. Also the f(x) symbol can be represented by the y symbol. What about linear equations ? Linear equations are represented by a line and the graph of a non linear function is not a line. Are all linear equations functions? All linear equations will meet the requirement of a function, by using the horizontal line test. That´s not true, vertical lines have a linear equation (x=a) and the graph does not pass the vertical line test (x=a is not a function) Is there an instance when a linear equation is not a function? There are no instances where a linear equation is not a function. As long as it passes the linear line test it is a function. This is wrong, as we said vertical lines have a linear equations but is not a function Support your answer: To test a function you can use the vertical line test, If the vertical line crosses the line in 2 or more points, then the equation is not a function . If x=a is a vertical line and we select the point x=a , the vertical line crosses the graph of x=a in infinitely many points so vertical lines does not pass the vertical line test so vertical lines are not functions Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate. 3 x ² +4 ² = 16 2x ² - 3y ² = 5 Here are 2 nonlinear equations but there aren´t inputs We can modify the answer: Equation: f(x)=3x^2+16, inputs: 2 and 3 Answer: f(2)=3(22)+16=12-16=-4; f(3)= 3(32)+16=27-16=11 Student 2: A common trait for both functions and linear equations is that they both can be considered to be equations, but a function consists of a domain and a range, that corresponds to exactly one member. Another difference between the two would be that functions don't have to look like straight lines when you graph them, but linear equations are straight lines. Linear equations like y=ax+b (a 0) have a domain and range too (real numbers), I agree with the second part, functons don´t have to look like straight lines. Not every linear equation is a function. For example, vertical lines are not functions, since for any input value there are multiple output values. Vertical lines fail the "vertical line" test, which says that a vertical line must cross a function at most one time. I agree with this part too, we can say that vertical lines are the only kind of linear equations that are not a function. Example: f(x) = x^2 - 3 Inputs 0 and -10 Problem is right. We can add a problem: f(x)=x7-1, inputs 2 and -2 Solve Problem: f(x)= x+3 This is a linear equation, but is not clear what we have to solve