Graphs of polynomial functions

Front

What is the domain of a polynomial function?

Back

The domain of a polynomial function is always (-∞, +∞).

Front

What are the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3)?

Back

The zeros are -4, -1, and 3.

Front

Describe the end behavior of a polynomial function where the leading coefficient is positive and the degree is even.

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

Front

Describe the end behavior of a polynomial function where the leading coefficient is negative and the degree is odd.

Back

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞.

Front

What is a relative maximum in the context of polynomial functions?

Back

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

Front

What is another term for 'where a function crosses the x-axis'?

Back

x-intercept, zero, or root.

Front

What is the degree of the polynomial function y = 2x^3 - 5x + 4?

Back

The degree is 3.

Front

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

Back

Set the polynomial equal to zero and solve for x.

Front

What does it mean if a polynomial has a double root?

Back

It means the root is repeated, and the graph touches the x-axis at that point but does not cross it.

Front

What is the leading coefficient of the polynomial y = -4x^5 + 2x^3 - x + 7?

Back

The leading coefficient is -4.