Graphing Functions and Linear Equations

This video tutorial introduces function notation in the context of linear functions, explaining how to evaluate function values by substituting inputs into the function equation. It demonstrates solving for specific outputs by setting the function equal to a desired value and solving for x. The tutorial includes examples of graphing function values to verify results and concludes with a graphical example to reinforce the concepts. The video aims to provide a comprehensive understanding of function notation and its application in linear functions.

What is the general form of a linear function?

• f(x) = ax^2 + bx + c

• f(x) = mx + b

• f(x) = a/x + b

• f(x) = ax^3 + bx^2 + cx + d

In the function f(x) = mx + b, what does 'm' represent?

• The constant term

• The y-intercept

• The slope

• The x-intercept

What is the value of f(0) for the function f(x) = 3x + 1?

• 1

• 3

• 0

• 4

How do you find f(5) for the function f(x) = 3x + 1?

• Substitute 5 for y and solve

• Substitute 5 for x and solve

• Set f(x) to 5 and solve for x

• Set f(x) to 5 and solve for y

What is the output of f(-1) for the function f(x) = 3x + 1?

• 0

• -2

• 1

• 2

If f(x) = 3x + 1, what input gives an output of 0?

• 1/3

• -1/3

• 0

• 3

For the function f(x) = 3x + 1, what input results in an output of 10?

• 3

• 2

• 3.5

• 4

What is the x-value when f(x) = 0 for the function f(x) = 3x + 1?

• 0

• -1/3

• 1/3

• 1

What is the x-value when f(x) = 10 for the function f(x) = 3x + 1?

• 4

• 3

• 5

• 2

Which point is on the line of the function f(x) = 3x + 1?

• (1, 0)

• (0, 1)

• (1, 1)

• (0, 0)