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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?
Can the graph of a polynomial function have no y-intercept?
No, the graph of a polynomial function cannot have no y-intercept. A polynomial function is defined for all real numbers, and when you evaluate it at (x = 0), you get the y-intercept, which is the value of the function at that point. Thus, every polynomial function will intersect the y-axis at least once, ensuring it has a y-intercept.
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.
How do you find the y intercepts for a polynomial function?
To find the y-intercepts of a polynomial function, set the value of ( x ) to 0 and solve for ( y ). This involves substituting 0 into the polynomial equation and simplifying to find the corresponding ( y )-value. The y-intercept is the point where the graph of the function crosses the y-axis, represented as the coordinate (0, ( y )).
Can the exponents in a polynomial function be negative?
No. It would not be a polynomial function then.
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.
