End behavior

Front

What is end behavior in polynomial functions?

Back

End behavior refers to the behavior of the graph of a polynomial function as the input values (x) approach positive or negative infinity.

Front

How does the degree of a polynomial affect its end behavior?

Back

The degree of a polynomial determines the direction in which the graph rises or falls at the ends. Even degrees lead to the same end behavior on both sides, while odd degrees lead to opposite end behaviors.

Front

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

Back

The end behavior will be up/up, meaning the graph rises on both ends.

Front

What is the end behavior of a polynomial function with an even degree and a negative leading coefficient?

Back

The end behavior will be down/down, meaning the graph falls on both ends.

Front

What is the end behavior of a polynomial function with an odd degree and a positive leading coefficient?

Back

The end behavior will be down/up, meaning the graph falls on the left and rises on the right.

Front

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

Back

The end behavior will be up/down, meaning the graph rises on the left and falls on the right.

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

How do you determine the degree of the polynomial m(x)=3x-4x^4+9x+12?

Back

The degree is determined by identifying the highest exponent, which in this case is 4.

Front

What is a horizontal compression in the context of function transformations?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor greater than 1, causing the graph to be 'squeezed' towards the y-axis.

Front

In the function g(x)=f(2x-5)+3, what does the '2' represent?

Back

The '2' represents a horizontal compression of the function f(x) by a factor of 1/2.