Understanding Linear Functions

The video tutorial demonstrates how to determine the input values of a linear function given specific output values. It covers solving the function algebraically and verifying the solutions graphically. Two examples are provided: solving f(x)=0 and f(x)=-4 for the function f(x)=-2x+6. The tutorial also shows how to use a graphing calculator to verify solutions.

What is the first step in solving for the input when the output is zero in a linear function?

• Subtract the constant term from both sides

• Add the constant term to both sides

• Multiply both sides by the coefficient of x

• Divide both sides by the coefficient of x

What is the input value when the output of the function f(x) = -2x + 6 is zero?

• x = 0

• x = 2

• x = 6

• x = 3

How can you verify the solution graphically for the function f(x) = -2x + 6 when the output is zero?

• Check if the line passes through (0, 6)

• Check if the line passes through (6, 0)

• Check if the line passes through (3, 0)

• Check if the line passes through (0, 3)

In the second example, what output value are we solving for?

• -4

• 6

• -2

• 0

What is the input value when the output of the function f(x) = -2x + 6 is -4?

• x = 2

• x = 5

• x = 3

• x = 4

How can you verify the solution graphically for the function f(x) = -2x + 6 when the output is -4?

• Check if the line passes through (5, -4)

• Check if the line passes through (5, 0)

• Check if the line passes through (4, -5)

• Check if the line passes through (3, -4)

What feature of the graphing calculator is used to verify the solutions?

• Function plotter

• Equation solver

• Table feature

• Graph feature

What should be the table start value when setting up the graphing calculator for verification?

• 0

• 1

• -1

• 5

What is the x-value when the y-value is zero in the table feature of the graphing calculator?

• x = 5

• x = -4

• x = 0

• x = 3

What is the x-value when the y-value is -4 in the table feature of the graphing calculator?

• x = -4

• x = 5

• x = 3

• x = 0