Understanding Linear and Exponential Functions

The video tutorial explains how to determine if a function is linear or exponential by analyzing patterns in a table of values. It demonstrates how to identify a linear function through repeated addition and calculate the slope using ordered pairs. The tutorial then guides viewers on writing the linear equation in slope-intercept form and verifies it graphically by plotting points on a coordinate plane.

What pattern in function values indicates a linear function?

• Repeated division

• Repeated multiplication

• Repeated subtraction

• Repeated addition

What is the form of a linear function equation?

• f(x) = x^2 + bx + c

• f(x) = ax^2 + bx + c

• f(x) = a^x

• f(x) = mx + b

What does the 'b' represent in the linear function equation f(x) = mx + b?

• The slope

• The x-intercept

• The vertical intercept

• The horizontal intercept

How is the slope of a linear function calculated?

• Change in input divided by change in output

• Change in output divided by change in input

• Product of inputs and outputs

• Sum of inputs and outputs

What is the slope if the output increases by 2 and the input increases by 5?

• 2

• 1/2

• 5/2

• 2/5

Which ordered pairs are used to verify the slope calculation?

• (0, 0) and (5, 5)

• (0, -3) and (5, -1)

• (1, 2) and (3, 4)

• (2, 3) and (4, 5)

What is the simplified form of the slope formula?

• x1 - x2 / y1 - y2

• y1 - y2 / x1 - x2

• x2 - x1 / y2 - y1

• y2 - y1 / x2 - x1

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

• f(x) = 2/5x - 3

• f(x) = 5/2x - 3

• f(x) = 2/5x + 3

• f(x) = 5/2x + 3

How can the equation of the linear function be verified graphically?

• By checking if the line passes through the origin

• By ensuring the line is horizontal

• By confirming all points from the table lie on the line

• By checking if the line is vertical

What does the slope of 2/5 indicate about the function's behavior?

• The output decreases by 5 for every 2 increase in input

• The output increases by 2 for every 5 increase in input

• The output increases by 5 for every 2 increase in input

• The output decreases by 2 for every 5 increase in input