JustAnswer



What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate.

|A function is almost always confused with an equation and most students of Math may not appreciate a very clear distinction between the two. An equation has no |

|special notation to identify it, whereas a function is denoted by letters such as f, g, h, (, F etc. |

|[If we have only one function to discuss, we usually use the notation “f” meaning “function”] |

|Consider f(x) = 8x + 5 |

|This is a linear function. You can think of a function as a machine that takes in a number, does some sort of work on it, and puts it out as another number at the |

|other end of the machine. In this case, you put in some number x; the function multiplies it by 8, then adds 5 to the result, and puts out this new number, which |

|is called f(x). |

|If you give that new number (the output of the function) the name y, then you have your familiar linear equation in slope-intercept form: y = 8x + 5. |

|A function is only allowed to put out one number for each number that goes in. If you think about a vertical line such as x = 3, you can't make this into a |

|function. You can only put in the number 3, and any number can come out. [The point (5, y) is on the line for any value of y.] A function isn't allowed to do this.|

|Therefore, a linear function is never graphed by a vertical line. The slope-intercept form can describe any linear function. |

|A function always outputs a value. Suppose the function |

|f(x) = 10x + 20, what this means is that this function outputs different values for different input values of variable 'x'. For example: f(10) = 10 ( 10 + 20 = |

|120, |

|f(20) = 10 ( 20 + 20 = 220. i.e. we substitute different values into x and get different outputs. The important point is that every function outputs a value. |

| |

|An example of a nonlinear function is f(x) = x^2 – 10 and the corresponding nonlinear equation is y = x^2 – 10. |

|Solution: x^2 – 10 = 0 ( x^2 = 10 ( x = (10 = {-3.162, 3.162} (Approximately) |

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.

|Equations define the relationship between one or more variables. For example: |

|x² ( 10x = 0 is a single variable equation, whereas 2x + 3y = 10 is a multi variable equation. An equation doesn’t output a value. We can solve the equation and |

|find out the values of the variables. The equation would be valid only for certain values of the variables. |

|A function is always an equation, but not all equations are functions. For an equation, each abscissa (x-coordinate) may have one or more distinct ordinates |

|(y-coordinates)... For a function, each abscissa may have only one ordinate. For example, x = 10 is an equation but not a function |

|For a function, if you use a vertical line test, the line will cross the graph of a function in exactly one point...For an equation, the line will cross the graph |

|of an equation in one or more points. |

| |

|Some more intricate nonlinear functions are g(x) = e^x and h(x) = log 3 x and the corresponding nonlinear equations are y = e^x and is y = log 3 x. |

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download