By Reed S.
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Extra info for More Mathematics Than Science
Example text
Now, this method of evaluating the output value of a polynomial can be captured in a type of short-hand notation by positioning the input value and the coefficients of the polynomial in a certain form. Again, consider this polynomial: f(x) = 4x3 - 3x2 + x - 4 We will picture it evaluated at the input value x = 2. Arrange the input value, the coefficients, and a line like this: 2) 4 -3 1 -4 Now drop down the 4: 2) 4 -3 1 -4 4 Multiply the input 2 times the 4. Place this product, 8, under the -3: 2) 4 -3 1 -4 8 4 Add the -3 and the 8.
A small negative input will output a large negative value, and a large negative input will output a small negative value. Here is a picture showing this idea: This makes complete sense if you think about it for a moment. Consider a large positive input value, say one million, i. , 1,000,000. The output of f(x) = 1/x would be one millionth, i. 000001. 000001 (or -1/1,000,000) -1,000,000 Let us look at this function as it leaves the graph at the top and bottom. You should notice that the green function line approaches, but does not touch, the y-axis.
The second term here is made up of two factors, e and f. So, considering the original expression: (a + b + c)(d - ef) One could correctly say that the second term of the second factor is ef. Taking it just a bit further, the second factor of the second term of the second factor of the original expression is f. Linear Functions Linear functions are functions that have x as the input variable, and x is raised only to the first power. Such functions look like the ones in the above graphic. Notice that x is raised to the power of 1 in each equation.