4-2 Graphing Polynomials

Front

What is the end behavior of a polynomial function when the leading coefficient is positive and the degree is even?

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

What is the end behavior of a polynomial function when the leading coefficient is negative and the degree is odd?

Back

As x → ∞, y → -∞ and as x → -∞, y → ∞.

Front

Define relative maximum in the context of polynomial functions.

Back

A relative maximum is a point on the graph where the function value is higher than all nearby points.

Front

Define relative minimum in the context of polynomial functions.

Back

A relative minimum is a point on the graph where the function value is lower than all nearby points.

Front

What does it mean if a polynomial function is increasing on an interval?

Back

The function's output values are rising as the input values increase within that interval.

Front

What does it mean if a polynomial function is decreasing on an interval?

Back

The function's output values are falling as the input values increase within that interval.

Front

How do you determine the x-intercepts of a polynomial function?

Back

Set the polynomial equal to zero and solve for x.

Front

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

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x=0.

Front

What is the degree of a polynomial, and why is it important?

Back

The degree is the highest power of x in the polynomial, determining the graph's end behavior and the number of x-intercepts.

Front

What is a turning point in a polynomial graph?

Back

A turning point is where the graph changes direction from increasing to decreasing or vice versa.