End Behavior of Functions

This lesson covers the end behavior of functions, focusing on polynomial and exponential functions. It explains how the leading term determines the end behavior of polynomial functions and how the base of an exponential function indicates growth or decay. The lesson includes examples and applications to help classify and describe these functions.

What are the two main types of functions discussed in this lesson?

• Polynomial and exponential functions

• Trigonometric and logarithmic functions

• Rational and irrational functions

• Linear and quadratic functions

In a polynomial function, what determines the end behavior?

• The middle term

• The smallest term

• The leading term

• The constant term

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

• As x approaches infinity, y approaches negative infinity

• As x approaches negative infinity, y approaches positive infinity

• As x approaches infinity, y approaches infinity

• As x approaches negative infinity, y approaches zero

What happens to y in the exponential function y = 2^x as x becomes very large?

• y becomes negative

• y remains constant

• y approaches zero

• y approaches infinity

In the function y = 2^x, what is the behavior of y as x becomes very negative?

• y approaches infinity

• y becomes negative

• y approaches zero

• y remains constant

What is the base condition for an exponential function to represent decay?

• Base between 0 and 1

• Base greater than 1

• Base equal to 1

• Base less than 0

How does the end behavior of exponential decay differ from exponential growth?

• Both approach infinity as x approaches infinity

• Decay approaches zero as x approaches infinity

• Growth approaches zero as x approaches infinity

• Both approach zero as x approaches infinity

When classifying a function, what indicates that it is exponential?

• x is in the base

• x is in the exponent

• The function has a linear term

• The function has a constant term

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

• As x approaches negative infinity, y approaches zero

• As x approaches infinity, y approaches infinity

• As x approaches negative infinity, y approaches infinity

• As x approaches infinity, y approaches negative infinity

In the context of this lesson, what is the significance of the leading term in a polynomial function?

• It determines the function's periodicity

• It determines the function's end behavior

• It determines the function's intercepts

• It determines the function's symmetry