End Behavior of Exponential Functions

The video tutorial explains the concept of end behavior in exponential functions, focusing on how graphs behave as x approaches positive and negative infinity. It covers both growth and decay functions, illustrating how to graph them and interpret their end behavior. The tutorial also discusses vertical shifts in graphs and how they affect the asymptote. Examples are provided to demonstrate these concepts, emphasizing the importance of understanding the asymptote's role in predicting end behavior.

What is the general form of an exponential function?

• y = a^bx

• y = ab^x

• y = a + bx

• y = ax^b

What does 'end behavior' refer to in the context of exponential functions?

• The behavior of the function at x = 0

• The behavior of the function as x approaches infinity or negative infinity

• The slope of the function

• The y-intercept of the function

What is the significance of the base 'b' in the exponential function y = ab^x?

• It determines the y-intercept

• It affects the growth or decay rate

• It changes the x-intercept

• It has no effect on the function

What is the role of the constant 'a' in the exponential function y = ab^x?

• It determines the slope

• It affects the y-intercept

• It has no effect on the function

• It changes the x-intercept

In the end behavior formula, what does f(x) represent?

• The x-values

• The y-values

• The slope

• The asymptote

As x approaches positive infinity, what are we predicting in terms of y-values?

• Whether y-values increase or decrease

• The x-intercept

• The exact y-value at infinity

• The slope of the tangent line

What is the significance of the asymptote in determining end behavior?

• It is the maximum value of the function

• It acts as a boundary that the graph approaches but never crosses

• It determines the x-intercept

• It is the minimum value of the function

How does the base 'b' affect the function when b > 1?

• The function remains constant

• The function decays

• The function grows

• The function oscillates

For the function y = 3^x, what happens to y as x approaches negative infinity?

• y approaches infinity

• y remains constant

• y approaches zero

• y approaches negative infinity

What is the end behavior of y = 3^x as x approaches positive infinity?

• y approaches infinity

• y approaches zero

• y approaches negative infinity

• y remains constant