Unit 2 Review: Key Concepts and Practice Questions

In this AP calculus session, Becky Barnes and Jamal Sadiki explore exponential and logarithmic functions. They discuss exponential decay, solving exponential equations, and inverse functions. The session includes a review of logarithmic properties and concludes with a practical example. The instructors use a mix of explanations and problem-solving to enhance understanding.

What is the end behavior of a function exhibiting exponential decay as x approaches positive infinity?

• Remains constant

• Approaches positive infinity

• Approaches negative infinity

• Approaches zero

In the general form of an exponential function, what does the base 'B' represent?

• The common ratio

• The constant term

• The initial value

• The exponent

Which of the following is true for exponential growth?

• B value is less than one

• Output values decrease

• B value is greater than one

• A value is zero

How can you find the initial value 'a' in an exponential function from a graph?

• It's the y-intercept of the graph

• It's the slope of the graph

• It's the x-value when y is zero

• It's the y-value when x is zero

What does an inverse function do to the inputs and outputs?

• Switches them

• Halves them

• Squares them

• Doubles them

What is the inverse function of y = 3^x?

• y = log base 3 of x

• y = 3 * x

• y = x / 3

• y = x^3

How does a logarithm transform a product inside its argument?

• Turns it into a difference

• Keeps it as a product

• Turns it into a sum

• Turns it into a quotient

What is log base 2 of 8?

• 1

• 4

• 2

• 3

What is the result of log base 5 of 1?

• 1

• 5

• 0

• Undefined

What does the logarithmic property log base b of (x/y) simplify to?

• log base b of x - log base b of y

• log base b of x + log base b of y

• log base b of x / log base b of y

• log base b of x * log base b of y