Function Representation Practice: Graph & Algebraic Problems

Master graphical and algebraic representations of functions with step-by-step practice problems. Learn to graph linear functions, find equations, and interpret function graphs.

📚What You'll Master in Function Representation Practice
  • Graph linear functions using slope-intercept form and point-slope method
  • Find algebraic equations of lines given slope and coordinates
  • Identify points on function graphs and verify coordinate solutions
  • Convert between different representations of the same function
  • Determine parallel line equations with given constraints
  • Interpret graphical data to solve real-world function problems

Understanding Graphical Representation of a Function

Complete explanation with examples

As we learned in an article on functions, the standard "correspondence rule" is a connection between a dependent variable (Y) (Y) and an independent variable (X) (X) .

By means of a graph or drawing, which gives a visual aspect to the concept of the function. From the graph it is possible to understand whether it is a linear function (straight line), a quadratic function (parabola) and more.

Remember that when it comes to a graphical representation of a function, each point in the domain X X will always have only one point within the range Y Y . Therefore, not every drawing is a graphical representation of a function. Here is an example.

A1 - Graphical representation of a function

Detailed explanation

Practice Graphical Representation of a Function

Test your knowledge with 12 quizzes

Which of the following equations corresponds to the function represented in the graph?

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444000

Examples with solutions for Graphical Representation of a Function

Step-by-step solutions included
Exercise #1

Determine whether the following table represents a function

XY-1015811

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 constant change in Y values, meaning an increase of 3

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

Answer:

Yes

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:

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 #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

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
Exercise #5

Determine whether the given graph is 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

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

Video Solution

Frequently Asked Questions

Everything you need to know about Graphical Representation of a Function

How do I graph a linear function step by step?

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Start with the function equation like y = mx + b. Create a table of values by choosing x-values and calculating corresponding y-values. Plot these coordinate points on the Cartesian plane and connect them with a straight line.

What's the difference between slope-intercept and point-slope form?

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Slope-intercept form is y = mx + b where m is slope and b is y-intercept. Point-slope form is y - y₁ = m(x - x₁) where (x₁, y₁) is a known point and m is the slope. Both represent the same linear function.

How do I find the equation of a line passing through a point?

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Use the formula y = mx + b. Substitute the known slope (m) and the coordinates of the given point for x and y. Solve for b (y-intercept), then write the complete equation.

What makes two lines parallel in function representation?

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Parallel lines have identical slopes but different y-intercepts. If one line has equation y = 2x + 5, a parallel line would be y = 2x + k where k ≠ 5.

How can I tell if a graph represents a function?

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Use the vertical line test: if any vertical line intersects the graph at more than one point, it's not a function. Each x-value must correspond to exactly one y-value.

What are the main types of function graphs I should know?

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Key function types include: • Constant functions (horizontal lines) • Linear functions (straight diagonal lines) • Quadratic functions (parabolas) • Cubic functions (S-shaped curves) • Exponential functions (curved growth/decay)

How do I verify if a point lies on a function graph?

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Substitute the x-coordinate into the function equation and calculate the result. If the calculated y-value matches the y-coordinate of the point, then the point lies on the graph.

What's the easiest way to practice function representations?

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Start with simple linear functions, create value tables, plot points, and verify your graphs. Practice converting between algebraic equations and graphical representations using different slopes and intercepts.

More Graphical Representation of a Function Questions

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

Representations of Functions

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 Identify the Correct Equation: Linking X and Y with Table Data

Continue Your Math Journey

Master Graphical Representation 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 TablesAlgebraic Representation of a FunctionNotation 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