Graphical Representation of a Function - Examples, Exercises and Solutions

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

Practice Graphical Representation of a Function

Exercise #1

Is the given graph a function?

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Video Solution

Answer

Yes

Exercise #2

Is the given graph a function?

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Video Solution

Answer

No

Exercise #3

Is the given graph a function?

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Video Solution

Answer

Yes

Exercise #4

Is the given graph a function?

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Video Solution

Answer

No

Exercise #5

Is the given graph a function?

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Video Solution

Answer

No

Exercise #1

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

Answer

Yes

Exercise #2

Is the given graph a function?

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Video Solution

Answer

Yes

Exercise #3

Determine whether the following table represents a function

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Video Solution

Answer

Yes

Exercise #4

Determine whether the following table represents a function

XY-226101416111621

Video Solution

Answer

Yes

Exercise #5

Determine whether the following table represents a function

XY-101247

Video Solution

Answer

No

Exercise #1

Determine whether the following table represents a function

XY-1015811

Video Solution

Answer

Yes

Exercise #2

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

XY012348

Video Solution

Answer

No

Exercise #3

Determine whether the following table represents a function

XY-126123

Video Solution

Answer

No

Exercise #4

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

XY-2024601234

Video Solution

Answer

y=12x+1 y=\frac{1}{2}x+1

Exercise #5

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

XY-1012312345

Video Solution

Answer

y=x+2 y=x+2

Topics learned in later sections

  1. Ways to represent a function
  2. Representing a Function Verbally and with Tables
  3. Algebraic Representation of a Function
  4. Notation of a Function
  5. Rate of Change of a Function
  6. Variation of a Function
  7. Rate of change represented with steps in the graph of the function
  8. Rate of change of a function represented graphically
  9. Constant Rate of Change
  10. Variable Rate of Change
  11. Rate of Change of a Function Represented by a Table of Values
  12. Functions for Seventh Grade
  13. Increasing and Decreasing Intervals (Functions)
  14. Increasing functions
  15. Decreasing function
  16. Constant Function
  17. Decreasing Interval of a function
  18. Increasing Intervals of a function
  19. Domain of a Function
  20. Indefinite integral
  21. Inputing Values into a Function