Notation of a Function

🏆Practice representations of functions

The notation of a function actually refers to determining the "name" of the function.

It is customary to symbolize a function using letters from the Latin alphabet when the two most common notations are:

  • yy
  • f(x)f(x)

(Of course, similar notations can also be used).

The - inside parentheses expresses that it is an independent variable of the function and the function's dependency ( or ) on it. xx,yy,ff

Notation of a Function

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einstein

Determine whether the data in the following table represent a constant function

XY012348

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Examples and exercises with solutions of function notation

Exercise #1

Determine whether the data in the following table represent a constant function

XY012348

Video Solution

Step-by-Step Solution

It should be remembered that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can see that there is a constant change in X values, meaning an increase of 1, and a non-constant change in Y values - sometimes increasing by 1 and sometimes by 4

Therefore, according to the rule, the table does not describe a function

Answer

No

Exercise #2

Determine whether the following table represents a function

XY-1015811

Video Solution

Step-by-Step Solution

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can see that there is a constant change in X values, meaning an increase of 1, and a constant change in Y values, meaning an increase of 3

Therefore, according to the rule, the table describes a function.

Answer

Yes

Exercise #3

Determine whether the following table represents a function

XY02468-3-3-3-3-3

Video Solution

Step-by-Step Solution

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can see that there is a constant change in the X values, specifically an increase of 2, and the Y value remains constant.

Therefore, according to the rule, the table describes a constant function.

Answer

Yes

Exercise #4

Does the graph below represent a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

Video Solution

Step-by-Step Solution

It is important to remember that a function is an equation that assigns to each value in domain x x only one value in range y y .

Since we can see that for every x x value found on the graph there is only one correspondingy y value, the graph is indeed a function.

Answer

Yes

Exercise #5

Is the given graph a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

Video Solution

Step-by-Step Solution

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

We should note that for every X value found on the graph, there is one and only one corresponding Y value.

Therefore, the graph is indeed a function.

Answer

Yes

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