Graphing Higher-Degree Polynomials: Techniques and Zeros

What is a key challenge in graphing higher-degree polynomials compared to lines and parabolas?

• Plotting points is time-consuming and their behavior is less predictable.

• They always have the same shape.

• Their behavior is more predictable.

• They have no zeroes.

What does the leading coefficient test help determine?

• The number of zeroes of the function.

• The end behavior of the function.

• The exact maxima and minima of the function.

• The Y-intercept of the function.

If the leading coefficient of a polynomial with an odd exponent is positive, what is the end behavior?

• Falls on both sides.

• Rises on both sides.

• Rises to the left and falls to the right.

• Falls to the left and rises to the right.

How can the zeroes of a polynomial function be found?

• By determining the end behavior.

• By using the leading coefficient test.

• By setting the function equal to zero and solving for X.

• By finding the Y-intercept.

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What is the significance of zeroes in graphing polynomial functions?

• They indicate the maxima and minima.

• They determine the end behavior.

• They are the points where the function crosses the Y-axis.

• They are the points where the function equals zero and crosses the X-axis.

What information is needed to sketch a polynomial function?

• The Y-intercept only.

• The zeroes, end behavior, and multiplicity of each zero.

• Only the end behavior of the function.

• Only the zeroes of the function.

What happens if a zero is listed twice in the factors of a polynomial?

• The function will have no zeroes.

• The function will have an undefined behavior.

• The function will touch the X-axis at that value and then turn around.

• The function will cross the X-axis at that value.

What is the end behavior of a polynomial with an even exponent and a negative leading coefficient?

• Falls on both sides.

• Rises to the left and falls to the right.

• Falls to the left and rises to the right.

• Rises on both sides.

How can the Y-intercept of a polynomial function be found?

• By determining the end behavior.

• By finding the zeroes of the function.

• By setting X to zero and solving for Y.

• By using the leading coefficient test.

What does it mean if a zero has an odd multiplicity?

• The function will have no zeroes.

• The function will cross the X-axis at that point.

• The function will have an undefined behavior.

• The function will touch the X-axis at that point and turn around.