Exponential Functions Concepts and Applications

The video introduces a new unit on exponential functions, covering their features, transformations, and practical applications. Important announcements about grades and STAAR testing are made. The teacher explains exponential growth through a penny-doubling example and discusses the general form and characteristics of exponential functions. Transformations and their effects on graphs are also covered, followed by practice problems.

What is the new unit that the class is starting?

• Rational Functions

• Linear Functions

• Quadratic Functions

• Exponential Functions

When is the last day to submit missing assignments for this nine-week grading period?

• Next Friday

• Next Monday

• This Wednesday

• This Friday

In the example given, how much money would you have after 26 days if you start with one penny and double it every day?

• $1,500,000

• $1,000,000

• $671,088.64

• $500,000

What is the general form of an exponential function?

• y = ax^2 + bx + c

• y = mx + b

• y = a/x

• y = b^x

Which of the following is NOT a common base for exponential functions?

• e

• 10

• 5

• 2

What happens to the graph of an exponential function if the base is a fraction?

• It becomes a straight line

• It becomes exponential decay

• It curves upwards

• It remains unchanged

What transformation occurs when you add a constant to the exponent of an exponential function?

• The graph shifts left

• The graph shifts down

• The graph shifts right

• The graph shifts up

What does a negative sign in front of the base of an exponential function indicate?

• Reflection over the y-axis

• Vertical compression

• Reflection over the x-axis

• Vertical stretch

If an exponential function is vertically compressed, what can be said about the coefficient in front of the base?

• It is greater than 1

• It is negative

• It is equal to 1

• It is less than 1

What is the equation of the asymptote for the function g(x) = 3 * 2^(x-1) + 11?

• y = 3

• y = 2

• y = 11

• y = 1