Exploring Graphs of Exponential Functions

This video tutorial covers exponential functions, including their definition, properties, and graphing techniques. It explains exponential growth and decay, highlighting the characteristics of each. The tutorial also explores the symmetry and reflection of exponential functions and discusses real-life applications such as population growth and radioactive decay.

What is the base of an exponential function if f(x) = b^x and b is greater than 0 but not equal to 1?

• The coefficient

• The base

• The exponent

• The variable

If b is between 0 and 1 in an exponential function f(x) = b^x, what type of function is it?

• Quadratic function

• Linear function

• Exponential decay

• Exponential growth

What is the y-intercept of the function f(x) = 2^x?

• (0, 2)

• (0, 1)

• (1, 0)

• (0, 0)

What happens to the value of f(x) = 2^x as x approaches negative infinity?

• It approaches 1

• It approaches 2

• It approaches infinity

• It approaches 0

In the function f(x) = (1/2)^x, what is the value of f(-1)?

• 1/4

• 1/2

• 2

• 4

What is the horizontal asymptote of the function f(x) = (1/2)^x?

• y = 1

• y = 0

• y = -1

• y = x

What is the relationship between the graphs of f(x) = 2^x and f(x) = 2^-x?

• They are translations

• They are reflections across the x-axis

• They are reflections across the y-axis

• They are identical

Which of the following is an example of exponential growth?

• Cooling of a hot object

• Population growth

• Medication dosage

• Radioactive decay

Which of the following is an example of exponential decay?

• Radioactive decay

• Population growth

• Internet users growth

• Bacteria growth

What is the website mentioned for exploring population growth?

• mathworld.com

• intmath.com

• populationgrowth.com

• exponentialfunctions.com