Understanding Linear and Exponential Functions

The video tutorial explains how to determine if a function is linear or exponential by analyzing a table of values. It demonstrates how to derive the equation of a linear function in the form f(x) = mx + b, where m is the slope and b is the y-intercept. The tutorial includes calculating the slope using ordered pairs and verifying the function graphically to ensure accuracy.

What is the main difference between a linear and an exponential function?

• Linear functions have a pattern of repeated multiplication, while exponential functions have a pattern of repeated addition.

• Linear functions have a pattern of repeated addition, while exponential functions have a pattern of repeated multiplication.

• Linear functions are always increasing, while exponential functions can decrease.

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

In the given table, what pattern indicates that the function is linear?

• The function values increase by 2 each time.

• The function values decrease by 2 each time.

• The function values are divided by 2.

• The function values are multiplied by 2.

What is the form of a linear function equation?

• f(x) = x^2 + bx + c

• f(x) = a^x

• f(x) = mx + b

• f(x) = ax^2 + bx + c

How do you determine the vertical intercept 'b' from the table?

• By subtracting the first x-value from the first y-value.

• By finding the last function value in the table.

• By calculating the average of all function values.

• By finding the first function value when x is zero.

What is the formula for calculating the slope 'm'?

• m = (x2 - x1) / (y2 - y1)

• m = (y2 - y1) / (x2 - x1)

• m = (y1 - y2) / (x1 - x2)

• m = (x1 - x2) / (y1 - y2)

Why is it important to use the formula for slope calculation?

• To find the maximum value of the function.

• To accurately determine the change in output relative to the change in input.

• To verify the function is exponential.

• To ensure the slope is always positive.

What is the slope of the function in the given table?

• -2

• 2

• 0

• -1

What does the graph of the function verify?

• The function has no intercept.

• The function equation matches the points in the table.

• The function is quadratic.

• The function is exponential.

How can you verify the slope using the graph?

• By ensuring the line goes up two units and left one unit.

• By checking if the line is vertical.

• By ensuring the line goes down two units and right one unit.

• By checking if the line is horizontal.

What is the equation of the linear function derived from the table?

• f(x) = 2x + 5

• f(x) = -2x - 5

• f(x) = x^2 - 5

• f(x) = -x + 5