Exponential Functions and Graph Behavior

The video tutorial covers exponential graphs, starting with y = a^x where a > 1, explaining their behavior and characteristics. It then discusses the graph of y = 1^x, which is a horizontal line. The tutorial moves on to graphs where 0 < a < 1, showing how they decrease and approach the x-axis. It also covers graphs of y = a^(-x), explaining their reflection properties. The video includes examples of sketching graphs like y = 4 * 3^x and y = 20 * 2^(-x), and solving for a and b in equations like y = a * b^x.

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

• 3

• 2

• 1

• 0

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

• It grows faster on the right

• It grows slower on the right

• It decreases faster on the left

• It is a horizontal line

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

• A downward curve

• A horizontal line

• A vertical line

• An upward curve

For a base between 0 and 1, how does the graph behave as x increases?

• It increases

• It oscillates

• It decreases

• It remains constant

What transformation occurs when the exponent in y = a^(-x) is negative?

• Reflection in the y-axis

• Translation downwards

• Reflection in the x-axis

• Translation upwards

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

• It is a reflection in the y-axis

• It is a vertical line

• It is a reflection in the x-axis

• It is a horizontal line

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

• 12

• 4

• 3

• 1

In the equation y = 20 * 2^(-x), what happens to the graph as x increases?

• It approaches the y-axis

• It approaches the x-axis

• It becomes a horizontal line

• It becomes a vertical line

Given the point (0, 3) on the graph y = a * b^x, what is the value of 'a'?

• 3

• 1

• 2

• 4

If the point (2, 90) lies on the graph y = a * b^x, and a = 10, what is b?

• 5

• 3

• 2

• 4