AP Precalculus - Unit 1 - Part A

Front

What is the end behavior of the function \( f(x) = -2x^7 + 5x^4 + 6x^2 - 3 \) as \( x \) approaches infinity?

Back

\( \lim_{x \rightarrow \infty} f(x) = -\infty \) because the leading term is negative and has an odd degree.

Front

Define Absolute Maximum in the context of a function's graph.

Back

The Absolute Maximum is the highest point over the entire domain of the function.

Front

Define Absolute Minimum in the context of a function's graph.

Back

The Absolute Minimum is the lowest point over the entire domain of the function.

Front

What is a Local Maximum?

Back

A Local Maximum is a point where the function value is higher than all nearby points.

Front

What is a Local Minimum?

Back

A Local Minimum is a point where the function value is lower than all nearby points.

Front

What does it mean for a root to have a multiplicity of 2?

Back

A root with a multiplicity of 2 means that the root is repeated twice, indicating a touchpoint on the x-axis.

Front

How do you determine if a function is increasing at a decreasing rate?

Back

A function is increasing at a decreasing rate when its first derivative is positive and its second derivative is negative.

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

What does it mean for a function to have an even degree?

Back

A function has an even degree if the highest power of \( x \) in the polynomial is even, which affects its end behavior.

Front

What is the relationship between the degree of a polynomial and its number of roots?

Back

A polynomial of degree \( n \) can have up to \( n \) roots.