g(x) = 2 The function can be written as f(x) = a where a = 2. Because > 1, the graph of y = 2 is the graph of y = that is stretched vertically. b. g(x) = – – 3 The negative sign causes a reflection across the x-axis. Then a dilation occurs in which a = and a translation in which k = –3. So the graph of g(x) = – – 3 is reflected
Polynomials Description Examples Description In Maple, polynomials are created from names, integers, and This is a univariate polynomial in the variable x with integer coefficients. Multivariate polynomials, and polynomials over other number rings and fields are constructed similarly.
Practice using function transformations, small changes to an equation that translate, dilate or reflect the function's graph. Exponential Functions Discover how exponential functions, in which a variable appears in the exponent, are used to model real-world situations.
There exist algebraic formulas for the roots of cubic and quartic polynomials, but these are generally too cumbersome to apply by hand. Even worse, it is known that there is no algebraic formula for the roots of a general polynomial of degree at least 5. In practice, the roots of the characteristic polynomial are found numerically by computer ...
Polynomial graphing calculator This page help you to explore polynomials of degrees up to 4. It can calculate and graph the roots (x-intercepts), signs , Local Maxima and Minima , Increasing and Decreasing Intervals , Points of Inflection and Concave Up/Down intervals .
= (2x + 3)(5x3º 9x2ºx +4) Multiply the first factor by 2. Repeat the steps above for g(x) = 5x3º 9x2ºx +4. Any zero of g will also be a zero of ƒ. The possible rational zeros of g are x =±1, ±2, ±4, ±1 5, ±2 5, and ±4 5. The graph of ƒ shows that 4 5 may be a zero.} 4 5} is a zero. So ƒ(x)=(2x + 3) x º}4 5} (5x2 º 5x º5)=(2x + 3)(5x º 4)(x2 º x º1).
Description Lesson 5.2 Evaluate and Graph Polynomial Functions Lesson 5.3 Add, Subtract, and Multiply Polynomials
The zeros of a function are found by determining what x-values will cause the y-value to be equal to zero. One way to find the zeros is to graph the function on a graphing calculator to see what the x-coordinates are where the function intersects the x-axis.