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Functions Worksheet You have been hired as a consultant for Business Finder GPS. Programmers are making adjustments to improve the current software, and they have informed the owner of the company that they must use mathematical functions in their programming. They explained that they would like to discuss some options for updates with the owner and will be showing him both function notation and graphs.

The owner wants to make sure he understands the concept of a function before he talks to the programmers and has asked for your help. He sent you the following questions for you to answer: ● What is a function and how do you write function notation? ● How can I test if a graph is a function?

What is a function and how do you write function notation?

1. Provide a definition of a function.

A relationship between dependent and independent variables is referred to as a function. It is a mathematical expression rule. Notation is just the function of substituting any arithmetic value into an expression and then calculating it.[CITATION Funnd \l 2057 ] 2. Provide a graph of a function and a graph that isn’t a function. Explain why each graph is or isn’t a function. Note: To create the graphs, you can draw the graphs by hand. You can also use an online tool and place a screenshot of your graphs in the boxes below.

Provide a graph of a function here. Explain why this graph is considered a function.

This graph is functional because it’s demonstrated that the value f(x)=4 and the line only touches point on the graph.

Provide a graph that does not show a function here. Explain why this graph is not considered a function.

The graph is not a functional because of the vertical touches the graph very many times.

3. Convert the following equations into function notation (f(x) =).

Equation

Function Notation

y=x

F(y)

→x

3 y=2 x

F(x)

→2 x 3

f(x)

→ x-3

f(x)

→ 0−x

y +3=x x+ y=0

y−x=5

F(x) →5+ x

2 y+ x =4 y −3 x

F(x)

f(x)=2x

→2 x

How can I test if a graph is a function?

1. Describe how you can test if a graph is a function or not.

The vertical line must be above and overstrike for the graph to be functional. this is the technical method to determine whether the graph is functional.

If the vertical line crosses the graph at more than one point or location, the graph cannot be considered functional. This is one method of determining whether the graph is not functional.

2. Apply the vertical line test to the following graphs and determine which ones are functions.

A. The graph is a functional because its bypass only one on the graph.

B. The graph is a function because its only crosses or touch only one on the graph.

C. The graph is a function because the vertical line didn’t cross more than one position.

D. This graph is not a function because the line crosses over very many times.

E. This graph is a function because the line only bypass at one position

F. This graph is also a function because the line only bypass at one position

G. The graph is a functional because the line touches the line only one time

H. The graph is a function because the line pass through only at one position

A. the graph can not qualify to a function because the line struck very many positions or points.

B. The graph is a function because the vertical line tested at a single position only

References Function. (2022, 8 23). From Encyclopædia Britannica: https://www.britannica.com/science/function-mathematics