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Quizzes > Mathematics

Vertical Line Test: Is This Graph a Function?

Quick math quiz to check which graphs are functions. Instant results.

Editorial: Review CompletedCreated By: Mamang PulobiUpdated Aug 28, 2025
Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Is It a Function math trivia quiz for high school students.

Use this quiz to decide if a graph is a function using the vertical line test. Work through 20 quick items with lines and curves, see instant feedback, and spot common non-function graph examples. Keep building skills with graphing functions practice, explore families with a parent functions test, and review key ideas in a properties of functions quiz.

Which of the following best describes a function in mathematical terms?
A relation where every input has exactly one output
A relation that has at least one input with no output
A relation that assigns multiple outputs to a single input
A relation where every output has exactly one input
A function is defined as a relation where each input is associated with exactly one output. This is why the first option correctly describes a function.
In the vertical line test, what does it mean if a vertical line intersects a graph at more than one point?
The graph represents a quadratic function
The graph does not represent a function
The graph represents a function
The graph represents a linear equation
If any vertical line intersects a graph at more than one point, it indicates that an input corresponds to multiple outputs. Therefore, the graph does not represent a function.
Which of the following graphs would pass the vertical line test?
A vertical line
A parabola opening sideways
A non-vertical straight line
A circle
A non-vertical straight line ensures every vertical line intersects it exactly once, satisfying the function definition. The other graphs fail the vertical line test.
If a set of ordered pairs includes (2, 3), (2, 5), and (3, 4), is it a function?
No, because the input 2 is paired with more than one output
Yes, because each output is paired with an input
No, because the ordered pairs are not sorted
Yes, because the inputs are listed in order
A function requires every input to have only one output. Since the input 2 is paired with both 3 and 5, it violates the definition of a function.
A mapping diagram shows inputs {1, 2, 3} mapping to outputs {4, 5, 6} respectively. Does this diagram represent a function?
No, because the outputs form a sequence
Yes, because each input has a unique output
Yes, because the outputs are larger than the inputs
No, because the diagram does not show the rule
Since every input in the mapping diagram has exactly one output, it meets the criteria for a function. The sequential nature of outputs is not relevant to the definition.
Which of the following diagrams fails to represent a function?
A diagram where different inputs share the same output
A diagram where each input arrow points to exactly one output
A diagram where an input points to multiple outputs
A diagram with all outputs unique
A diagram where an input is connected to more than one output violates the core definition of a function. Each input must correspond to exactly one output.
If the equation y² = x is graphed, does it represent a function?
No, because the equation is not linear
Yes, because each x has at least one y value
Yes, because it forms a symmetrical graph
No, because some x values have two corresponding y values
For x > 0, the equation y² = x gives two y values, one positive and one negative, thereby failing the function criteria. Thus, it does not represent a function.
Consider a graph that consists of two intersecting lines. Does it represent a function?
No, because a vertical line through the intersection would cross the graph twice
Yes, because the lines intersect at a single point
No, because intersecting lines are never functions
Yes, because both lines are straight
When two lines intersect, there exists at least one vertical line that will intersect both lines at the point of intersection. This violates the function rule of one output per input.
A horizontally opening parabola described by x = y² is graphed. Is this graph a function of x?
No, because some x values have two corresponding y values
Yes, because it is a parabola
Yes, because the graph is symmetric
No, because it does not pass the horizontal line test
The equation x = y² results in two y values for a given positive x value, thus violating the definition of a function when considering x as the independent variable. Therefore, it is not a function of x.
Which algebraic graph represents a function?
y² = x + 2
y² = x
y = |x|
x = 3
The graph of y = |x| assigns a unique y value for each x, making it a function. The other equations either define vertical lines or yield multiple y values for some x.
What does the vertical line test determine for a graph?
It determines if the graph is symmetric about the y-axis
It checks if any vertical line intersects the graph more than once
It determines the slope of the graph
It identifies horizontal asymptotes
The vertical line test is a visual method to determine whether a graph represents a function by checking if any vertical line intersects it more than once. This ensures that every input has a unique output.
Which set of ordered pairs represents a function?
{(2, 4), (2, 5), (3, 5)}
{(1, 3), (2, 3), (1, 5)}
{(1, 2), (2, 3), (1, 4)}
{(2, 5), (3, 6), (4, 7)}
A function requires that each input appears only once with a unique output. Option B meets this criterion, while the others have repeated inputs with different outputs.
A graph of a function is symmetric about the y-axis. What type of function is it likely to be?
A periodic function
A linear function
An even function
An odd function
Symmetry about the y-axis is a hallmark of even functions, meaning that f(x) = f(-x). This makes option B the correct answer.
Which statement is true about linear functions?
Linear functions always contain curves
A linear function always passes the vertical line test
All linear functions are quadratic
A vertical line always represents a linear function
Linear functions produce straight lines which inherently pass the vertical line test. This confirms that they are valid functions.
A graph shows a curve with a distinct turning point that passes the vertical line test. Which type of function could this be?
A quadratic function
A circle
A vertical line
A hyperbola
A quadratic function typically has a parabolic shape with a turning point and passes the vertical line test. The other options do not meet these criteria.
Consider the piecewise function defined as: for x < 0, y = -x, and for x ≥ 0, y = x. Does this graph represent a function?
Yes, because it is symmetric about the y-axis
No, because the function switches between two rules
Yes, because each x value has a unique output
No, because piecewise functions are not functions
Even though the function is defined in pieces, each x value in the domain corresponds to exactly one output. This satisfies the definition of a function.
A function f(x) is defined graphically with a small gap (hole) in the curve. Does the presence of this hole mean the graph is not a function?
Yes, because functions must be continuous
No, because holes are a feature of all functions
No, because a hole does not cause any input to have more than one output
Yes, because a hole indicates a missing output
A hole in the graph represents a removable discontinuity and does not imply that an input has more than one output. Therefore, the graph still represents a function.
The equation y = √(x²) is graphed. Does this graph represent a function?
Yes, because it simplifies to |x|, which passes the vertical line test
No, because absolute value functions are not continuous
Yes, because every x gives two y values
No, because square roots normally yield two values
The equation y = √(x²) simplifies to |x|, which assigns a unique nonnegative value for each x, adhering to the definition of a function. Therefore, it passes the vertical line test.
When a graph is defined by an absolute value equation such as y = |2x - 3|, why does it represent a function?
Because absolute value functions provide two outputs for each x
Because absolute value equations are always quadratic
Because the absolute value yields a single nonnegative output for every x
Because the graph is symmetric about the x-axis
The absolute value operation ensures that for every x, there is only one nonnegative y value. This property guarantees that the equation defines a function.
Consider the function f(x) = 1/(x - 2). Which statement accurately describes its graph?
It represents a function that is symmetric about the y-axis
It represents a function with a vertical asymptote at x = 2
It represents a function that is discontinuous at x = 0
It represents a function defined for all real numbers
The function f(x) = 1/(x - 2) is undefined at x = 2, which creates a vertical asymptote. This is the correct description of its behavior.
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Study Outcomes

  1. Analyze graphical representations to identify key characteristics of functions.
  2. Apply the vertical line test to determine if a graph qualifies as a function.
  3. Evaluate various graphs to differentiate between functions and non-functions.
  4. Interpret the relationship between inputs and outputs in graphical depictions.
  5. Assess the effectiveness of using graphical tests in verifying function properties.

Quiz: Does This Graph Represent a Function? Cheat Sheet

  1. Definition of a Function - A function is like a trusty vending machine: each input (your button press) leads to exactly one output (your snack), with no surprises. Understanding this one-to-one correspondence is key to mastering algebraic relationships.
  2. Master the Vertical Line Test - If any vertical line you draw crosses a graph more than once, that graph isn't a function. This quick visual trick is your secret weapon for spotting valid functions in a flash.
  3. Practice with Parabolas, Circles & Ellipses - Try the test on different shapes: parabolas always pass, circles always fail, and ellipses depend on their orientation. Seeing these examples helps you recognize patterns like a true graph guru.
  4. Linear Equations Are Your Friends - Equations in the form y = mx + b always sail right through the Vertical Line Test because each x gives you a unique y. Knowing this lets you breeze through straight-line graphs.
  5. Spot the Exception: Vertical Lines - Graphs defined by x = a (vertical lines) crash the test by intersecting at infinitely many points, so they're not functions. It's an important quirk that keeps you sharp during graph analysis.
  6. Universal Application - Whether you're looking at trigonometric curves, exponential growth, or piecewise plots, the Vertical Line Test works every time. It's the universal checklist for function status.
  7. Many-to-One vs. One-to-Many - Functions can map many different x-values to the same y-value (that's allowed), but never the other way around. Grasping this distinction helps you avoid common pitfalls.
  8. Real-World Graphs - Apply the Vertical Line Test to things like population-versus-time or temperature charts to see if they behave as functions. Bringing theory into real data makes learning stick!
  9. Sketch & Test - Grab a pencil, draw your own crazy curves, and run the Vertical Line Test on them. This hands-on practice solidifies your understanding and builds confidence.
  10. Blend Visuals with Definitions - While the Vertical Line Test is awesome, always pair it with the formal definition of a function for deeper insight. This dual approach makes you a function-analysis pro.
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