Graphs of Polynomials

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the direction of the graph as x approaches positive or negative infinity.

Front

How do you find the y-intercept of a polynomial function?

Back

To find the y-intercept, substitute x = 0 into the polynomial function and solve for y.

Front

What does it mean for a polynomial function to be even?

Back

A polynomial function is even if f(-x) = f(x) for all x in its domain, resulting in symmetry about the y-axis.

Front

What does it mean for a polynomial function to be odd?

Back

A polynomial function is odd if f(-x) = -f(x) for all x in its domain, resulting in symmetry about the origin.

Front

What is the degree of a polynomial?

Back

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

Front

What is the end behavior of a polynomial function?

Back

End behavior describes how the values of f(x) behave as x approaches positive or negative infinity.

Front

How does the leading coefficient affect the end behavior of a polynomial?

Back

If the leading coefficient is positive, the graph rises to the right; if negative, it falls to the right.

Front

What is a cubic function?

Back

A cubic function is a polynomial of degree three, typically in the form f(x) = ax^3 + bx^2 + cx + d.

Front

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

Back

The y-intercept is the point where the graph crosses the y-axis, indicating the value of the function when x = 0.

Front

How can you determine if a polynomial function has a maximum or minimum?

Back

You can determine maxima or minima by finding the critical points using the first derivative test.