Linear and Exponential Function Concepts

The video tutorial explores how to identify different types of functions—linear, exponential, and quadratic—using tables of values. It explains the characteristics of each function type, including how to recognize them through patterns in the data. The tutorial also covers how to derive both recursive and explicit equations for exponential and linear functions, and provides examples to illustrate these concepts.

What is the main characteristic of a linear function when looking at a table of values?

• The values are multiplied by a constant.

• The values are added by a constant.

• The values are divided by a constant.

• The values form a parabola.

In an exponential function, how do you determine the next term in a sequence?

• Add a constant to the previous term.

• Multiply the previous term by a constant.

• Divide the previous term by a constant.

• Subtract a constant from the previous term.

What is a recursive equation in the context of exponential functions?

• An equation that uses a constant to find the next term.

• An equation that uses the first term to find all other terms.

• An equation that uses the previous term to find the next term.

• An equation that uses the last term to find the previous term.

How do you find the 'a' value in an explicit exponential equation?

• By adding the constant to the first term.

• By dividing the first term by the constant.

• By multiplying the first term by the constant.

• By finding the value at x equals zero.

What indicates a quadratic function when analyzing a table of values?

• The values are all the same.

• The values decrease by a constant amount.

• The values form a symmetrical pattern.

• The values increase by a constant amount.

Which equation represents a quadratic function?

• y = ax^2 + bx + c

• y = a^x

• y = mx + b

• y = x + c

What is the main feature of a linear function's recursive equation?

• It adds a constant to the previous term.

• It divides the previous term by a constant.

• It subtracts a constant from the previous term.

• It multiplies the previous term by a constant.

How do you determine the y-intercept in a linear function's explicit equation?

• By adding the slope to the first term.

• By multiplying the slope by the first term.

• By finding the value at x equals zero.

• By subtracting the slope from the first term.

What is the slope in a linear function's explicit equation?

• The constant multiplied by each term.

• The constant subtracted from each term.

• The constant added to each term.

• The constant divided by each term.

Which of the following is NOT a characteristic of exponential functions?

• The values form a straight line.

• The values are multiplied by a constant.

• The values have a constant ratio.

• The values increase rapidly.