Exponential Functions Concepts Review

Mr. Tarrou introduces graphing exponential functions, starting with the parent function y=2^x. He explains negative and zero exponents, graphing techniques, and differentiates between exponential growth and decay. Key characteristics like asymptotes, domain, and range are discussed. Transformations such as shifts and reflections are explored, concluding with a reflection and decay example.

What is the value of 2 raised to the power of 0?

• 0

• 1

• 2

• Undefined

Which point does the basic exponential function y = a^x always pass through?

• (1,1)

• (0,0)

• (0,1)

• (1,0)

What is the horizontal asymptote of the basic exponential function y = a^x?

• y = 1

• y = 0

• x = 0

• x = 1

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

• Shifted up by 2 units

• Shifted right by 2 units

• Shifted left by 2 units

• Shifted down by 2 units

What is the range of the function y = 2^x - 2?

• y > 0

• y < -2

• y > -2

• y < 0

What transformation occurs when a negative sign is placed in front of the exponent in y = 2^(-x)?

• Vertical shift

• Reflection over the y-axis

• Horizontal shift

• Reflection over the x-axis

What is the effect of a negative exponent on the base of an exponential function?

• Increases the base

• Flips the base

• Decreases the base

• Leaves the base unchanged

In the context of exponential functions, what does a base between 0 and 1 indicate?

• No change

• Undefined behavior

• Exponential decay

• Exponential growth

What happens to the graph of y = 2^x when it is reflected over the y-axis?

• It becomes y = 2^(-x)

• It becomes y = -2^x

• It shifts up

• It shifts down

What is the domain of the basic exponential function y = a^x?

• x > 0

• x < 0

• All real numbers

• x = 0