Understanding Functions and Graphs

This video tutorial covers the process of connecting different representations of functions. It begins with a description of the function f(x) and derives the formula f(x) = 2x + 5. The tutorial then demonstrates how to complete an input-output table using this formula and identifies a pattern in the outputs. The video proceeds to graph the function by plotting points from the table and analyzes the graph to identify key features such as intercepts. The lesson concludes with a summary of the linear nature of the function and its graphical representation.

What operation is performed first in the function f(x)?

• Dividing by two

• Subtracting three

• Doubling the input

• Adding five

What is the formula for the function f(x)?

• f(x) = 2x - 5

• f(x) = x * 5

• f(x) = x + 5

• f(x) = 2x + 5

What is the output when the input is -3?

• 3

• 0

• 1

• -1

How does the output change as the input increases by one?

• Decreases by one

• Increases by two

• Increases by one

• Decreases by two

What is the output for an input of 3?

• 11

• 9

• 7

• 5

Where are the inputs located on the graph?

• None of the above

• Horizontal axis

• Vertical axis

• Diagonal axis

What is the vertical intercept of the graph?

• (0, 5)

• (0, -5)

• (5, 0)

• (-2.5, 0)

What type of function is f(x) based on its graph?

• Cubic

• Quadratic

• Exponential

• Linear

What is the horizontal intercept of the graph?

• (-2.5, 0)

• (0, 5)

• (0, -2.5)

• (5, 0)

What is the output for an input of 0?

• 0

• 5

• 10

• 15