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A polynomial function have a polynomial graph.
... That's not very helpful is it, but the most common formal definition of a function is that it is its graph.
So, I can only describe it. A polynomial graph consists of "bumps", formally called local maxima and minima, and "inflection points", where concavity changes. What's more? They numbers and shape varies a lot for different polynomials. Usually, the poly with higher power will have more "bumps" and inflection points, but it is not a absolute trend.
The best way to analyze the graph of a polynomial is through Calculus.
What else can I help you with?
Use a graphing utility to graph the sine function and its polynomial approximation in the sme viewing window?
Yes, I did.
How do you graph a polynomial in order to solve for the Zeros?
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
Can the exponents in a polynomial function be negative?
No. It would not be a polynomial function then.
Are a polynomial's factors the values at which the graph of a polynomial meets the y-axis?
Not quite. The polynomial's linear factors are related - not equal to - the places where the graph meets the x-axis. For example, the polynomial x2 - 5x + 6, in factored form, is (x - 2) (x - 3). In this case, +2 and +3 are "zeroes" of the polynomial, i.e., the graph crosses the x-axis. That is, in an x-y graph, y = 0.
What is the graph of quadratic polynomial called?
A parabola.
Can the graph of a polynomial function have a vertical asymptote?
no
What do the zeros of a polynomial function represent on a graph?
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
how many roots does the graphed polynomial function have?
here is the graph
What is the definition for the zero of a polynomial function?
The zero of a polynomial in the variable x, is a value of x for which the polynomial is zero. It is a value where the graph of the polynomial intersects the x-axis.
What part of a polynomial function determines the shape and end behavior of a graph?
The order of the polynomial (the highest power) and the coefficient of the highest power.
How do you do a parabola?
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
What is a root in a polynomial graph?
A root is the value of the variable (usually, x) for which the polynomial is zero. Equivalently, a root is an x-value at which the graph crosses the x-axis.
Use a graphing utility to graph the sine function and its polynomial approximation in the sme viewing window?
Yes, I did.
How do you graph a polynomial in order to solve for the Zeros?
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
What does the s shaped line in the graph indicate?
That it is non-linear. If it is a graph of a polynomial, it would need to be a polynomial of odd order. But it could be the graph of the tangent function, or a combination of reciprocal functions over a limited domain. In fact the s shaped line, by itself, indicates very little.
What is the line graph in which the data points do not fallalong a straight line?
A non-linear graph. It could be a polynomial (of a degree greater than 1), a power function, a logarithmic or trigonometric graph. In fact any mathematical function other than a linear equation.
Can the exponents in a polynomial function be negative?
No. It would not be a polynomial function then.
