Understanding Exponential Functions and Transformations

The video tutorial covers exponential functions, focusing on their properties, graphing, and transformations. It explains how to sketch exponential graphs, apply transformations, and use function notation. The tutorial also discusses creating tables of values, understanding asymptotes, and determining the domain and range of exponential functions.

What is the defining characteristic of an exponential function?

• The variable is in the exponent.

• The function is a straight line.

• The variable is in the base.

• The function is a parabola.

How do you determine the value of 2 to the power of -3?

• 1/8

• 8

• 1/4

• 2

What is the asymptote of the function y = 2^x?

• x = 1

• x = 0

• y = 0

• y = 1

What happens to the graph of y = 2^x when it is transformed to y = 2^(x+1)?

• It shifts left by 1 unit.

• It shifts right by 1 unit.

• It shifts up by 1 unit.

• It shifts down by 1 unit.

In the transformation y = 3 * 2^x - 2, what does the '3' represent?

• Reflection

• Horizontal shift

• Vertical shift

• Vertical stretch

What is the effect of a negative sign in front of the function, such as in y = -2^x?

• Vertical stretch

• Horizontal shift

• Reflection over the x-axis

• Reflection over the y-axis

How does a vertical shift affect the asymptote of an exponential function?

• It changes the y-intercept.

• It changes the slope.

• It has no effect.

• It changes the position of the asymptote.

What is the function notation for a graph that has been shifted left by 1 and down by 2?

• f(x+1) - 2

• f(x-1) + 2

• f(x-1) - 2

• f(x+1) + 2

What is the domain of the function y = 2^x?

• All real numbers

• x is an integer

• x < 0

• x > 0

What is the range of the function y = 2^x after a vertical shift down by 2 units?

• y < -2

• y > 0

• y > -2

• y = -2