Polynomial Function Quiz

What is the definition of a polynomial function?

• A polynomial function is a function that has a square root in its equation.

• A polynomial function is a function that can only have one term.

• A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer and a_n, a_(n-1), ..., a_1, a_0 are constants.

• A polynomial function is a function that involves only odd powers of x.

Explain the difference between a polynomial function and a non-polynomial function.

• Polynomial functions are expressed as a sum of powers of a variable with non-negative integer exponents, while non-polynomial functions include trigonometric, exponential, and logarithmic functions.

• Polynomial functions are always linear, while non-polynomial functions can be quadratic.

• Polynomial functions are always continuous, while non-polynomial functions can be discontinuous.

• Polynomial functions involve only odd exponents, while non-polynomial functions involve only even exponents.

Describe the general form of a polynomial function.

• f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0 + b

• f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0 + c

• f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0 + d

• f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0

What is the leading coefficient of a polynomial function?

• Coefficient of the term with the middle degree

• Coefficient of the constant term

• Coefficient of the term with the highest degree

• Coefficient of the term with the lowest degree

How can you determine the degree of a polynomial function?

• Check the coefficient of the constant term in the polynomial.

• Look at the highest power of the variable in the polynomial.

• Count the number of terms in the polynomial.

• Look at the lowest power of the variable in the polynomial.

Explain the concept of end behavior in relation to the graph of a polynomial function.

• End behavior refers to the behavior of a function at the beginning of its graph

• End behavior is determined by the number of x-intercepts of the polynomial function

• End behavior of a polynomial function describes its behavior as x approaches positive or negative infinity based on the degree and leading coefficient of the polynomial.

• End behavior is only relevant for linear functions

What are the possible shapes of the graph of a polynomial function?

• Circular

• Spiral

• Linear, Quadratic, Cubic, Quartic, Quintic, etc.

• Rhombus

How do the roots of a polynomial function relate to its graph?

• The roots of a polynomial function correspond to the x-intercepts of its graph.

• The roots of a polynomial function are always positive

• The roots of a polynomial function are imaginary numbers

• The roots of a polynomial function are located at the maximum points of its graph

What is the significance of the y-intercept in the graph of a polynomial function?

• The y-intercept represents the value of the function when x is equal to zero.

• The y-intercept is always negative

• The y-intercept is the point where the function crosses the x-axis

• The y-intercept is the maximum value of the function

Discuss the role of turning points in the graph of a polynomial function.

• Turning points indicate the function is constant

• Turning points are irrelevant in polynomial functions

• Turning points in the graph of a polynomial function represent the local maximum or minimum points where the function changes direction.

• Turning points always occur at x = 0