Exponential Functions and Their Graphs

This video tutorial covers exponential graphs, starting with graphs where the base is greater than one, explaining their rapid increase and asymptotic behavior. It then discusses graphs with a base of one, which are horizontal lines, and those with a base between zero and one, which decrease towards the x-axis. The video also explores graphs with negative exponents, showing how they reflect across the y-axis. Several examples are provided, including sketching graphs using tables of values and solving for unknowns in equations of the form y = a * b^x using given points.

What is the y-intercept of the graph y = 2^x?

• 2

• 3

• 1

• 0

How does the graph of y = 3^x compare to y = 2^x?

• It increases more rapidly.

• It increases at the same rate.

• It increases more slowly.

• It decreases.

What is the shape of the graph y = 1^x?

• A vertical line at x = 1

• A horizontal line at y = 1

• A decreasing curve

• An increasing curve

For the graph y = (1/2)^x, what happens as x increases?

• The graph increases.

• The graph decreases.

• The graph remains constant.

• The graph oscillates.

What is the behavior of the graph y = (1/2)^x as x decreases?

• It oscillates.

• It remains constant.

• It approaches infinity.

• It approaches zero.

What transformation occurs when y = a^x is changed to y = a^(-x)?

• Translation upwards

• Reflection in the y-axis

• Translation downwards

• Reflection in the x-axis

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

• It is a translation to the right.

• It is a reflection in the x-axis.

• It is a translation to the left.

• It is a reflection in the y-axis.

What is the y-intercept of the graph y = 4 * 3^x?

• 1

• 3

• 4

• 12

In the graph y = 4 * 3^x, what happens as x increases?

• The graph oscillates.

• The graph increases rapidly.

• The graph remains constant.

• The graph decreases.

What is the y-intercept of the graph y = 20 * 2^(-x)?

• 20

• 10

• 0

• 40