End Behavior Review

Front

What does the notation \( \lim_{x\rightarrow\infty}f(x)=\infty \) indicate?

Back

It indicates that as x approaches infinity, the function f(x) increases without bound (to the right and up).

Front

If a function has a negative leading coefficient and an even degree, what is the end behavior?

Back

The end behavior is \( \lim_{x\rightarrow -\infty}f(x)=-\infty \) and \( \lim_{x\rightarrow \infty}f(x)=-\infty \).

Front

What does the notation \( \lim_{x\rightarrow -\infty}f(x)=-\infty \) mean?

Back

It means that as x approaches negative infinity, the function f(x) decreases without bound (to the left and down).

Front

For the function \( f(x)=-15x^5-9x^4-4x+12 \), what are the limit sentences?

Back

The limit sentences are \( \lim_{x\rightarrow -\infty}f(x)=\infty \) and \( \lim_{x\rightarrow \infty}f(x)=-\infty \).

Front

What does the notation \( f(x)=-\infty \) signify?

Back

It signifies that the function f(x) approaches negative infinity, indicating a downward trend.

Front

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

Back

The end behavior is \( \lim_{x\rightarrow -\infty}f(x)=-\infty \) and \( \lim_{x\rightarrow \infty}f(x)=\infty \).

Front

What does the notation \( \lim_{x\rightarrow\infty}f(x)=-\infty \) indicate?

Back

It indicates that as x approaches infinity, the function f(x) decreases without bound (to the right and down).

Front

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

Back

The end behavior is \( \lim_{x\rightarrow -\infty}f(x)=\infty \) and \( \lim_{x\rightarrow \infty}f(x)=\infty \).

Front

What is the significance of the leading coefficient in determining end behavior?

Back

The leading coefficient determines whether the ends of the graph rise or fall as x approaches positive or negative infinity.

Front

What does the notation \( \lim_{x\rightarrow -\infty}f(x)=\infty \) mean?

Back

It means that as x approaches negative infinity, the function f(x) increases without bound (to the left and up).