End Behavior of Functions

Front

What is the end behavior of a function?

Back

The end behavior of a function describes how the output (y) behaves as the input (x) approaches positive or negative infinity.

Front

As x approaches positive infinity, what does it mean if y approaches positive infinity?

Back

It means that the graph of the function rises indefinitely as x increases.

Front

As x approaches negative infinity, what does it mean if y approaches negative infinity?

Back

It means that the graph of the function falls indefinitely as x decreases.

Front

What does it indicate if a function approaches a finite value as x approaches infinity?

Back

It indicates that the function has a horizontal asymptote.

Front

For the function y = -3x^4 + 2x^2 - 8x + 9, what is the end behavior as x approaches negative infinity?

Back

y approaches negative infinity.

Front

What is the significance of the leading term in a polynomial function for end behavior?

Back

The leading term determines the end behavior of the polynomial as x approaches positive or negative infinity.

Front

If a polynomial function has an even degree and a positive leading coefficient, what is its end behavior?

Back

As x approaches both positive and negative infinity, y approaches positive infinity.

Front

If a polynomial function has an odd degree and a negative leading coefficient, what is its end behavior?

Back

As x approaches positive infinity, y approaches negative infinity, and as x approaches negative infinity, y approaches positive infinity.

Front

What does it mean if a function approaches a specific value as x approaches positive infinity?

Back

It means that the function stabilizes or levels off at that value.

Front

How can you determine the end behavior of a rational function?

Back

By analyzing the degrees of the numerator and denominator and their leading coefficients.