Understanding Linear and Exponential Functions

This video tutorial compares linear and exponential functions, focusing on their forms, properties, and graphical representations. It explains linear functions in slope-intercept form and exponential functions in general form. The tutorial uses tables of values to illustrate how linear functions increase by a constant amount, while exponential functions grow by a constant factor. It also discusses the domain and range of these functions and compares increasing and decreasing functions, highlighting exponential growth and decay.

What is the general form of a linear function?

• f(x) = mx + b

• f(x) = x^2 + bx + c

• f(x) = a * b^x

• f(x) = ax^2 + bx + c

In a linear function, what does the slope determine?

• The curvature of the graph

• The x-intercept

• The y-intercept

• The rate of change

What pattern do the outputs of a linear function follow?

• They remain constant

• They decrease by a constant percentage

• They double each time

• They increase by a constant amount

What is the general form of an exponential function?

• f(x) = x^2 + bx + c

• f(x) = mx + b

• f(x) = ax^2 + bx + c

• f(x) = a * b^x

How do the outputs of an exponential function change?

• They remain constant

• They double or multiply by a constant factor

• They increase by a constant amount

• They decrease by a constant amount

What is a key difference between linear and exponential functions?

• Both have a constant rate of change

• Linear functions have a constant factor of change, while exponential functions have a constant rate of change

• Both have a constant factor of change

• Linear functions have a constant rate of change, while exponential functions have a constant factor of change

What happens to a linear function when the slope is negative?

• The function oscillates

• The function increases

• The function decreases

• The function remains constant

What is the behavior of an exponential function when the base is greater than one?

• The function decreases linearly

• The function remains constant

• The function exhibits exponential decay

• The function exhibits exponential growth

What is the range of an exponential function with a base greater than one?

• y < 0

• y > 0

• y = 0

• y is all real numbers

What is the domain of both linear and exponential functions?

• Positive integers

• All real numbers

• Negative integers

• Non-negative integers