Differentiating Exponential and Linear Functions

This video tutorial explains how to recognize situations modeled by linear or exponential functions. It covers the properties of exponential functions, compares them with linear functions, and provides examples to illustrate these concepts. The video also includes a practical example of an exponential function and guides viewers on how to determine whether a function is linear or exponential using tables and graphs. The tutorial concludes with a preview of the next video, which will focus on writing and graphing exponential functions.

What is the basic form of an exponential function?

• y = a + bx

• y = ax + b

• y = a / bx

• y = a * b^x

In an exponential function, what condition must 'b' meet?

• b must not equal 1 and must be positive

• b must be a negative number

• b must be equal to 0

• b must be equal to 1

How does the graph of a linear function differ from that of an exponential function?

• Linear graphs are straight lines, while exponential graphs are curved.

• Exponential graphs can have negative y values, while linear graphs cannot.

• Linear graphs are curved, while exponential graphs are straight lines.

• Linear graphs have a constant rate of change, while exponential graphs do not.

In a linear function's table, where is the variable 'x' located?

• In the exponent

• In the base

• As a coefficient

• As a constant

What does 'a' represent in the exponential function form?

• The constant base

• The variable exponent

• The constant rate of change

• The initial value or y-intercept

What is the role of 'b' in an exponential function?

• It represents the y-intercept.

• It is the constant rate of change.

• It signifies the variable exponent.

• It is the multiplier or ratio.

If Jason quadruples his money every month starting with $17, what is the 'b' value in his exponential function?

• 0

• 1

• 4

• 17

How can you tell a function is linear based on its table values?

• The y values are multiplied by a constant factor.

• The x values are raised to a power.

• The difference between y values is constant.

• The y values are divided by a constant factor.

What does a constant rate of change in a table indicate about the function?

• It is exponential

• It is quadratic

• It is linear

• It is cubic

What indicates an exponential function when looking at a table?

• A constant ratio in y values

• A constant sum between x values

• A constant difference in x values

• A constant product in x values