Function Notation Practice Problems & Exercises f(x)

Master function notation with step-by-step practice problems. Learn f(x) notation, function naming conventions, and variable dependencies through guided exercises.

📚Master Function Notation Through Targeted Practice
  • Identify and write proper function notation using f(x) and y formats
  • Understand the meaning of independent variables in function expressions
  • Convert between different function notation styles and naming conventions
  • Recognize function dependency relationships and variable connections
  • Apply function notation rules to solve real-world mathematical problems
  • Build confidence in reading and interpreting mathematical function symbols

Understanding Notation of a Function

Complete explanation with examples

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

Detailed explanation

Practice Notation of a Function

Test your knowledge with 12 quizzes

Determine whether the following table represents a linear function

XY-126123

Examples with solutions for Notation of a Function

Step-by-step solutions included
Exercise #1

Determine whether the following table represents a constant function:

XY02468-3-3-3-3-3

Step-by-Step Solution

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

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

Therefore, the table does indeed describe a constant function.

Answer:

Yes, it does

Video Solution
Exercise #2

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

XY012348

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 observe 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

Video Solution
Exercise #3

Determine whether the following table represents a constant function

XY-101247

Step-by-Step Solution

To determine if the table represents a constant function, we need to examine the Y-values corresponding to the X-values given in the table.

  • Step 1: Identify the given values from the table. The pairs are as follows: - For X=−1X = -1, Y=2Y = 2 - For X=0X = 0, Y=4Y = 4 - For X=1X = 1, Y=7Y = 7
  • Step 2: Check if all Y-values are the same. Compare Y-values for each X-value:
    • - Y=2Y = 2 when X=−1X = -1, - Y=4Y = 4 when X=0X = 0, - Y=7Y = 7 when X=1X = 1.

Since the Y-values (2, 4, and 7) are not the same, the function is not constant.

Thus, the table does not represent a constant function. The correct choice is: No.

Answer:

No

Video Solution
Exercise #4

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

Step-by-Step Solution

To determine whether the graph represents a function, we apply the Vertical Line Test. Here are the steps we follow:

  • Step 1: Visualize placing a vertical line across various parts of the graph.
  • Step 2: Check if the vertical line intersects the graph at more than one point at any given position.

Step 1: On evaluating the given graph carefully, there is a notable presence of a vertical line passing through multiple y-values. Specifically, the vertical line goes from y=−3 y = -3 to y=3 y = 3 at x=3 x = 3 .

Step 2: Since this vertical line at x=3 x = 3 intersects the graph at an infinite number of points, it fails the Vertical Line Test.

Therefore, the graph does not represent a function. According to our analysis and the Vertical Line Test, the correct answer is No.

Answer:

No

Video Solution
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

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

Let's note that in the graph:

f(0)=2,f(0)=−2 f(0)=2,f(0)=-2

In other words, there are two values for the same number.

Therefore, the graph is not a function.

Answer:

No

Video Solution

Frequently Asked Questions

Everything you need to know about Notation of a Function

What is function notation and why do we use f(x)?

+
Function notation is a way to 'name' and represent functions using symbols like f(x) or y. The f represents the function name, while x inside parentheses shows the independent variable the function depends on. This notation helps us clearly identify which variable the function uses and makes mathematical expressions more organized.

What's the difference between y and f(x) notation?

+
Both y and f(x) represent the same concept - the output or dependent variable of a function. The main differences are: 1) f(x) explicitly shows the input variable (x), 2) f(x) allows for multiple functions using different letters (f, g, h), 3) y notation is simpler but less specific about dependencies.

How do you read f(x) out loud in mathematics?

+
f(x) is read as 'f of x' or 'f as a function of x.' This emphasizes that f depends on the value of x. Similarly, g(t) would be read as 'g of t' and h(y) as 'h of y.'

Can you use letters other than f for function notation?

+
Yes, you can use any letter from the Latin alphabet for function names. Common alternatives include g(x), h(x), P(t), V(r), and C(n). The choice often relates to the context - for example, C(n) might represent cost as a function of quantity n.

What does the x inside parentheses mean in f(x)?

+
The x inside parentheses represents the independent variable - the input value that the function depends on. It shows what variable you substitute into the function. When you see f(3), it means you're substituting 3 for x in the function f.

How do you write function notation for word problems?

+
Choose a letter that relates to what the function represents, then identify the independent variable. For example: 1) Area of a circle: A(r) where r is radius, 2) Population over time: P(t) where t is time, 3) Cost based on items: C(n) where n is number of items.

What are common mistakes students make with function notation?

+
Common errors include: confusing f(x) with multiplication (f × x), mixing up independent and dependent variables, using inconsistent variable names, and forgetting parentheses. Remember that f(x) represents the output value, not f times x.

When should I use function notation instead of regular equations?

+
Use function notation when you want to emphasize the relationship between variables, work with multiple functions simultaneously, or clearly identify inputs and outputs. It's especially helpful in calculus, when graphing multiple functions, or solving systems involving several related equations.

More Notation of a Function Questions

Click on any question to see the complete solution with step-by-step explanations

Representations of Functions

Linear Function: Match the Graph to its Correct Equation Match the Function Equation: Analyzing X-Y Values from -3 to 5 Graph to Equation Puzzle: Identify the Matching Function Decipher the Graph's Story: Which Equation Represents This Function? Equation Alignment for Table Mapping of X and Y

Continue Your Math Journey

Master Notation of a Function first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Ways to Represent a FunctionRepresenting a Function Verbally and with TablesGraphical Representation of a FunctionAlgebraic Representation of a FunctionRate of Change of a FunctionVariation of a FunctionRate of change represented with steps in the graph of the functionRate of change of a function represented graphicallyConstant Rate of ChangeVariable Rate of ChangeRate of Change of a Function Represented by a Table of ValuesFunctions for Seventh GradeIncreasing and Decreasing Intervals (Functions)Increasing functionsDecreasing functionConstant FunctionDecreasing Interval of a functionIncreasing Intervals of a functionDomain of a FunctionIndefinite integralInputing Values into a Function

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems
Creating a table from a verbal description Determine whether the table represents a function Is the graph an example of a function? Matching a graph to a function Matching a graph to a table Matching a table to a function Sketch the Graph from a Verbal Description