Front

What is a polynomial function?

Back

Front

How do you determine the intervals where a polynomial function is non-negative?

Back

To determine the intervals where a polynomial function is non-negative, perform a sign analysis by finding the roots of the polynomial, then test the sign of the function in the intervals defined by these roots.

Front

What is a horizontal asymptote?

Back

Front

What does it mean for a function to be concave up?

Back

A function is concave up on an interval if its graph lies above its tangent lines on that interval, indicating that the slope of the function is increasing.

Front

What is the average rate of change of a function?

Back

Front

How do you find vertical asymptotes of a function?

Back

Vertical asymptotes occur at values of x where the function approaches infinity, typically found by setting the denominator of a rational function to zero and solving for x.

Front

What is the significance of the roots of a polynomial function?

Back

The roots of a polynomial function are the values of x for which the function equals zero. They are important for determining the x-intercepts and the intervals where the function is positive or negative.

Front

What is the difference between a local maximum and a local minimum?

Back

A local maximum is a point where the function value is higher than all nearby points, while a local minimum is a point where the function value is lower than all nearby points.

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity, determined by the leading term of the polynomial.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial, which affects the shape of the graph and the number of roots.