Polynomial Graphs

How do you find the zeros of a polynomial function?

• Set the function equal to zero and solve for x.

• Differentiate the function and find critical points.

• Evaluate the function at various points until you find a zero.

• Factor the polynomial and find the roots.

How does the leading coefficient affect the graph of a polynomial?

• The leading coefficient determines the direction of the graph's ends: if positive, the right end rises; if negative, the right end falls.

• The leading coefficient affects the width of the graph: a larger coefficient makes the graph wider.

• The leading coefficient has no effect on the graph's shape or direction.

• The leading coefficient only affects the y-intercept of the graph.

What is the end behavior of the polynomial f(x) = 2x^3 - 4x + 1?

• As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches negative infinity.

• As x approaches positive infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.

• As x approaches positive infinity, f(x) approaches a constant value; as x approaches negative infinity, f(x) approaches a constant value.

• As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches a constant value.

What is the role of the constant term in a polynomial function?

• It determines the degree of the polynomial.

• It is the value of the polynomial when x = 0; it represents the y-intercept of the graph.

• It affects the shape of the graph but not the position.

• It is the coefficient of the highest degree term.

What does it mean for a polynomial to have zeros?

• Zeros of a polynomial are the values of x for which the polynomial equals zero; they represent the x-intercepts of the graph.

• Zeros of a polynomial are the coefficients of the polynomial.

• Zeros of a polynomial are the maximum values of the polynomial.

• Zeros of a polynomial are the points where the polynomial is undefined.

How can you determine the end behavior of a polynomial function?

• By analyzing its degree and leading coefficient.

• By finding its roots and critical points.

• By evaluating its value at x = 0.

• By graphing the function and observing its shape.

What is the difference between even and odd degree polynomials in terms of end behavior?

• Even degree polynomials have opposite end behavior (one end rises and the other falls), while odd degree polynomials have the same end behavior (both ends rise or both ends fall).

• Even degree polynomials have the same end behavior (both ends rise or both ends fall), while odd degree polynomials have opposite end behavior (one end rises and the other falls).

• Even degree polynomials always rise, while odd degree polynomials always fall.

• Even degree polynomials can have varying end behaviors, while odd degree polynomials always rise.

How can you verify if a polynomial function has a specific zero?

• Substitute the zero into the polynomial function; if the result is zero, then it is a valid zero.

• Graph the polynomial function and check if it crosses the x-axis at that point.

• Differentiate the polynomial function and check if the derivative is zero at that point.

• Evaluate the polynomial function at several points to see if it approaches zero.

What is the degree of a polynomial function?

• The degree of a polynomial function is the highest power of the variable in the polynomial.

• The degree of a polynomial function is the sum of the coefficients of the polynomial.

• The degree of a polynomial function is the number of terms in the polynomial.

• The degree of a polynomial function is always equal to zero.

What is the general form of a polynomial function?

• f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n is the leading coefficient and n is the degree.

• f(x) = a*x^2 + b*x + c, which is a quadratic function.

• f(x) = a*e^(bx), which is an exponential function.

• f(x) = a*x + b, which is a linear function.