Interpreting Graphical Behaviors Using Exponential Properties

This video tutorial covers the interpretation of exponential functions, including growth and decay, and their graphical behaviors. It explains transformations such as vertical stretching, compression, and reflection. The tutorial also delves into the properties of exponents and how they affect graph shifts. Additionally, it explores logistical growth functions, highlighting horizontal asymptotes and Y intercepts. By applying these concepts, viewers can better understand and sketch exponential graphs.

What happens to the graph of an exponential function when the base is greater than one?

• It represents exponential growth.

• It represents exponential decay.

• It becomes a constant function.

• It becomes a linear function.

How does a negative 'a' value affect the graph of an exponential function?

• It shifts the graph to the right.

• It reflects the graph vertically.

• It compresses the graph horizontally.

• It stretches the graph vertically.

What is the effect of a horizontal compression on the graph of an exponential function?

• The graph shifts upwards.

• The graph becomes narrower.

• The graph becomes wider.

• The graph shifts downwards.

How can you simplify an exponential expression with a negative exponent?

• By multiplying the base by zero.

• By adding the exponent to the base.

• By reciprocating the base.

• By subtracting the exponent from the base.

What does a horizontal asymptote represent in a logistical growth function?

• The rate of growth of the function.

• The initial value of the function.

• The minimum value the function can reach.

• The maximum value the function can reach.

In a logistical growth model, what happens to the function value as T becomes very large?

• It approaches zero.

• It becomes negative.

• It approaches the horizontal asymptote.

• It becomes infinite.

What is the Y-intercept of an exponential decay function?

• The initial value of the function.

• The point where the graph crosses the Y-axis.

• The point where the graph crosses the X-axis.

• The maximum value of the function.