Suppose you are looking at the graph of a function. a. What is the maximum numbe

Question

Suppose you are looking at the graph of a function. a. What is the maximum number of times that the graph canintersect the y-axis? Explain. b. Can the graph intersect the x-axis an infinite number oftimes? Explain c. If the function is a polynomial, how can you predict thenumber of times it might cross the x-axis? a. What is the maximum number of times that the graph canintersect the y-axis? Explain. b. Can the graph intersect the x-axis an infinite number oftimes? Explain c. If the function is a polynomial, how can you predict thenumber of times it might cross the x-axis? b. Can the graph intersect the x-axis an infinite number oftimes? Explain c. If the function is a polynomial, how can you predict thenumber of times it might cross the x-axis?

Explanation / Answer

When you draw a line on graph paper, with the line always moving tothe right, that is a graph of Y as a function of X. Since the linealways moves to the right, once it crosses the Y-axis it can't gotback. So it can cross the Y-axis only once. But the line can wiggle up and down as much as you want. So it cancross the X-axis any number of times, including an infinite numberof times. the polynomial function will have as many roots as the number ofits degree, providing that all the roots are real numbers. theroots include multiplicity. so it can have as many roots as itsdegree, or it can have less (even if all roots are real), or it canhave no real roots at all.

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