Comparing 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 covers the graphical behavior of these functions, highlighting the differences in their domains and ranges. The video concludes with a comparison of decreasing linear and exponential functions, emphasizing the concepts of negative slope and exponential decay.

What is the general form of a linear function?

• f(x) = a + bx

• f(x) = mx^2 + b

• f(x) = mx + b

• f(x) = a * b^x

What does the 'm' in the linear function formula represent?

• Exponent

• Y-intercept

• Base of the exponential function

• Slope of the line

In the context of the function f(x) = 2^x, what does the '2' represent?

• Exponent

• Y-intercept

• Slope

• Base of the exponential function

How do the outputs change in a linear function when the input increases by 1?

• Outputs increase by a constant amount

• Outputs decrease by a constant amount

• Outputs remain constant

• Outputs double

What pattern do the outputs of an exponential function follow?

• Increase by a constant amount

• None of the above

• Decrease by a constant amount

• Multiply by a constant factor

What is the domain of both linear and exponential functions?

• Integers only

• Negative real numbers

• All real numbers

• Positive real numbers

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

• Negative real numbers

• Integers only

• All real numbers

• Positive real numbers excluding zero

Which function type has a range of (0, infinity) when the function is increasing?

• Exponential with base less than one

• Exponential with base greater than one

• Linear with negative slope

• Linear with positive slope

What happens to the outputs of a linear function with a negative slope as inputs increase?

• Outputs increase

• Outputs remain constant

• Outputs become zero

• Outputs decrease

What describes the behavior of an exponential function with a base between zero and one?

• Exponential decay

• Linear growth

• Linear decay

• Exponential growth