Exponential Functions and Their Properties

The video tutorial covers the basics of exponential graphs, including their domains and ranges. It explains transformations using the I HOD and Over methods, focusing on vertical and horizontal shifts, as well as vertical stretch and reflection. The tutorial also discusses horizontal reflection in exponential graphs, providing examples and explanations for each transformation type.

What is a basic property of an exponential function's graph?

• It is a linear graph.

• It has a vertical asymptote.

• It has a horizontal asymptote at y = 0.

• It crosses the x-axis.

Why is the domain of an exponential function all real numbers?

• Because it only accepts positive numbers.

• Because it only accepts negative numbers.

• Because it can accept any real number as an exponent.

• Because it only accepts zero.

What is the range of a basic exponential function?

• All real numbers.

• Negative infinity to zero.

• Zero to positive infinity.

• Negative infinity to positive infinity.

What does the I HOD system help with?

• Identifying the domain of a function.

• Understanding transformations of graphs.

• Calculating the range of a function.

• Solving linear equations.

What happens to the graph of y = 2^x when you add 3 outside the exponential?

• It shifts 3 units downwards.

• It shifts 3 units upwards.

• It shifts 3 units to the right.

• It shifts 3 units to the left.

What is the new range when y = 2^x is shifted down by 4 units?

• Negative infinity to 4.

• Negative infinity to zero.

• Negative 4 to infinity.

• Zero to infinity.

How does the graph of y = 2^(x+1) differ from y = 2^x?

• It shifts 1 unit upwards.

• It shifts 1 unit to the left.

• It shifts 1 unit downwards.

• It shifts 1 unit to the right.

What is the effect of a horizontal shift to the right by 3 units on the domain?

• The domain changes to negative numbers only.

• The domain changes to positive numbers only.

• The domain changes to zero only.

• The domain remains all real numbers.

What happens to the graph of y = 3 * 2^x?

• It is compressed vertically.

• It is reflected over the x-axis.

• It is stretched vertically by a factor of 3.

• It is shifted horizontally.

What is the result of reflecting y = 2^x over the x-axis?

• The graph shifts upwards.

• The graph shifts downwards.

• The graph is reflected vertically.

• The graph is reflected horizontally.