End Behavior EOC Review

Front

What is end behavior in the context of graphing functions?

Back

End behavior describes the behavior of a function as the input values (x) approach positive or negative infinity. It helps to understand how the graph behaves at the extremes.

Front

Define the term 'as x approaches infinity'.

Back

'As x approaches infinity' means examining the behavior of a function as the x-values increase without bound.

Front

What does it mean when we say 'f(x) approaches infinity'?

Back

It means that the output values of the function (f(x)) increase without bound as x approaches a certain value or infinity.

Front

If a graph shows that as x → -∞, f(x) → +∞, what does this indicate?

Back

This indicates that the graph rises indefinitely as x moves towards negative infinity.

Front

What is the significance of the leading coefficient in polynomial functions regarding end behavior?

Back

The leading coefficient determines the direction of the graph's end behavior. If it's positive, the graph rises to the right; if negative, it falls to the right.

Front

For the function f(x) = 3x^4 + 2x - 5, what is the end behavior as x → ∞?

Back

As x → ∞, f(x) → ∞ because the leading term (3x^4) dominates the behavior of the function.

Front

What is the end behavior of the function f(x) = -2x^3 + 4?

Back

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

Front

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

Back

Analyze the degrees of the numerator and denominator. The end behavior is influenced by the leading terms of both.

Front

What does it mean if a function has a horizontal asymptote?

Back

A horizontal asymptote indicates the value that f(x) approaches as x approaches infinity or negative infinity.

Front

If a graph shows that as x → ∞, f(x) → -∞, what does this indicate?

Back

This indicates that the graph falls indefinitely as x moves towards positive infinity.