Graphing Exponential Functions: Key Concepts and Techniques

This video tutorial focuses on graphing exponential functions, explaining how to identify key points, horizontal asymptotes, and the domain and range of these functions. It covers specific examples, such as 1/3^x, 3^(x-2) + 1, and 5 - 2^(3-x), illustrating how to graph them and understand their properties. The tutorial also explores the generic shapes of exponential functions and their reflections across axes, providing a comprehensive understanding of how these functions behave graphically.

What is the value of any number raised to the power of zero?

• 0

• Undefined

• 1

• The number itself

What does the horizontal asymptote of a basic exponential function typically represent?

• y = 0

• x = 1

• y = 1

• x = 0

What is the domain of all exponential functions?

• All positive numbers

• All negative numbers

• All real numbers

• 0 to infinity

Why does the graph of an exponential function never touch the horizontal asymptote?

• It intersects at infinity

• It touches at zero

• It approaches but never touches

• It crosses over

How do you rewrite the function 1 over 3 raised to the x?

• x to the power 3

• 3 to the power -x

• -3 to the power x

• 3 to the power x

What is the range of the function 1 over 3 raised to the x?

• 0 to infinity

• -infinity to 0

• 0 to 1

• 1 to infinity

What is the new horizontal asymptote after the function is transformed by adding 1?

• y = 0

• y = -1

• y = 1

• y = 2

What is the effect of subtracting 2 from x in the function 3 raised to the (x-2)?

• Shifts right by 2 units

• Shifts left by 2 units

• Shifts up by 2 units

• Shifts down by 2 units

Which quadrant does the graph of 2 raised to the -x belong?

• Quadrant II

• Quadrant IV

• Quadrant I

• Quadrant III

What is the behavior of the graph of -2 raised to the x?

• Increases in Quadrant I

• Decreases in Quadrant II

• Increases in Quadrant IV

• Decreases in Quadrant III