Understanding Exponential Functions

The video tutorial explores graphing exponential functions using the Desmos calculator. It begins with graphing y=2^x and discusses the advantages of using Desmos over traditional calculators. The tutorial then examines the effects of changing the base of the exponential function, including bases greater than 1, bases between 0 and 1, and the impact of negative and positive multipliers on the graph's shape and growth rate.

What is one advantage of using the Desmos calculator over traditional calculators like the TI-81?

• It has a touchscreen interface.

• It is clumsier to use.

• It is more expensive.

• It cannot graph exponential functions.

When changing the base of an exponential function from 2 to 3e, what happens to the graph?

• It reflects over the x-axis.

• It grows at a slower rate.

• It maintains the same general shape but grows faster.

• It becomes a straight line.

How does the graph of y = 10^x compare to y = 2^x?

• It grows more slowly.

• It has the same growth rate.

• It grows more sharply.

• It does not intersect the y-axis.

What is the general shape of the graph when the base of the exponential function is changed?

• It becomes a straight line.

• It forms a circle.

• It remains an exponential curve.

• It becomes a parabola.

What is the effect of using a base greater than 1 in an exponential function?

• The graph becomes a straight line.

• The graph increases.

• The graph remains constant.

• The graph decreases.

What happens to the graph of y = (1/2)^x compared to y = 2^x?

• It does not intersect the x-axis.

• It grows faster.

• It is a mirror reflection along the y-axis.

• It becomes a horizontal line.

At x = 0, what is the value of y for both y = 2^x and y = (1/2)^x?

• 0

• 1

• 1/2

• 2

What is the value of y for y = (1/2)^x when x = 5?

• 5

• 1/32

• 32

• 1/2

What is the effect of using a base between 0 and 1 in an exponential function?

• The graph increases.

• The graph remains constant.

• The graph decreases.

• The graph becomes a straight line.

What happens to y = (1/2)^x when x is negative?

• It becomes the reciprocal of the positive x value.

• It becomes zero.

• It becomes undefined.

• It remains the same.