End Behavior

Front

What is end behavior in mathematics?

Back

End behavior describes the behavior of a function as the input values (x) approach positive or negative infinity.

Front

For the function y = -x^2, what is the end behavior?

Back

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

Front

What does it mean if a function's end behavior is 'down and down'?

Back

It means that as x approaches both negative and positive infinity, the function's output (y) decreases towards negative infinity.

Front

What is the end behavior of the function y = x^4 + 3x^3 - 4x + 1?

Back

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

Front

How do you determine the end behavior of a polynomial function?

Back

Look at the leading term of the polynomial. The sign and degree of the leading term determine the end behavior.

Front

What is the end behavior of the function y = -x^3 + 2x^2 + 3?

Back

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

Front

What does it indicate if a function's end behavior is 'up and down'?

Back

It indicates that as x approaches negative infinity, y approaches positive infinity, and as x approaches positive infinity, y approaches negative infinity.

Front

For the function y = x^5 - 4x^4 + 2x^2 - 1, what is the end behavior?

Back

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

Front

What is the significance of arrows on the ends of a graph?

Back

Arrows indicate the direction in which the graph continues, helping to determine the end behavior.

Front

If a function has end behavior 'As x → -∞, y → -∞' and 'As x → +∞, y → +∞', what can be inferred about its leading term?

Back

The leading term is positive and has an even degree.