Graphing Exponential Functions: Domain and Range Insights

This video tutorial covers graphing exponential functions, focusing on key features such as the y-intercept, asymptote, domain, and range. It introduces the concept of asymptotes, particularly horizontal asymptotes, and provides examples of graphing exponential growth and decay using a calculator. The video concludes with a summary of key takeaways and instructions for practice problems.

What is the new vocabulary word introduced in this section?

• Slope

• Vertex

• Asymptote

• Intercept

What is a horizontal asymptote in the context of exponential functions?

• A vertical line that the graph approaches

• A line that the graph approaches but never touches

• A point where the graph intersects the y-axis

• A line that the graph crosses multiple times

In Algebra 1, what is the horizontal asymptote for exponential functions?

• y = 1

• y = 0

• y = -1

• y = x

What is the first step in graphing an exponential function using a calculator?

• Turning on the calculator and entering the function

• Plotting points manually

• Drawing the x and y axes

• Identifying the y-intercept

What is the y-intercept of the function 3^x?

• 1

• 0

• 3

• 9

How do you determine if an exponential function represents growth?

• If the graph decreases from left to right

• If the value of b is between 0 and 1

• If the value of b is greater than 1

• If the graph is a straight line

What is the decay rate if the growth factor b is 0.5?

• 75%

• 100%

• 50%

• 25%

What is the y-intercept of the function 2 * (1/2)^x?

• 2

• 0

• 1

• 4

What is the domain of an exponential function in the form a * b^x?

• All real numbers

• All positive numbers

• All integers

• All negative numbers

If b is between 0 and 1, what does the exponential function represent?

• Constant

• Undefined

• Decay

• Growth