Exponential Functions and Their Graphs

This video tutorial covers the characteristics and sketching of exponential graphs, including those with bases greater than one, equal to one, and between zero and one. It explains the reflection of graphs with negative exponents and provides examples of sketching graphs using xy tables. The video also demonstrates solving for constants a and b in the equation y = a * b^x using given points on the graph.

What is the behavior of the graph y = 2^x as x becomes more negative?

• It approaches zero.

• It oscillates between positive and negative values.

• It approaches infinity.

• It becomes a horizontal line.

What is the graph of y = 1^x?

• A curve that approaches zero.

• A horizontal line at y = 1.

• A line passing through the origin.

• A vertical line at x = 1.

How does the graph of y = (1/2)^x behave as x increases?

• It increases exponentially.

• It decreases and approaches zero.

• It remains constant.

• It oscillates.

What transformation occurs when you graph y = 2^(-x) compared to y = 2^x?

• It reflects over the y-axis.

• It shifts up.

• It shifts down.

• It reflects over the x-axis.

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

• 4

• 3

• 12

• 1

For the graph y = 20 * 2^(-x), what is the value of y when x = 0?

• 10

• 40

• 0

• 20

In the equation y = a * b^x, if the point (0, 3) lies on the graph, what is the value of a?

• 1

• 3

• 0

• 2

Given the points (2, 90) and (5, 2430) on the graph y = a * b^x, what is the value of b?

• 4

• 2

• 3

• 5

If y = 3 * 2^x, what is the value of y when x = 4?

• 96

• 48

• 24

• 12

For the equation y = 10 * 3^x, what is the value of y when x = 2?

• 100

• 60

• 30

• 90