Representing a Function Verbally and with Tables - Examples, Exercises and Solutions

Function, describes a correlation or coincidence between a dependent variable (Y Y ) and an independent variable (X X ). The legitimacy of this relationship between the variables is called the " correspondence rule ".

Verbal representation of a function

The verbal representation of a function expresses the connection between variables verbally, i.e. through a story.

A typical verbal representation of a function can look like this:

  • Assuming that Daniel reads all the books he buys that month, the total number of books Daniel reads per year (Y Y ) is a function of the number of books Danny buys each month (X X ).

Tabular representation of a function

A tabular representation of a function is a demonstration of the legitimacy of a function using a table of values X X (independent variable) and the corresponding values Y Y (dependent variable).

In general, a table of values is shown as follows:

Verbal representation of a new function

Practice Representing a Function Verbally and with Tables

Exercise #1

Is the given graph a function?

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Video Solution

Answer

No

Exercise #2

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

No

Exercise #3

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

No

Exercise #4

Determine whether the following table represents a function

XY-101247

Video Solution

Answer

No

Exercise #5

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

XY012348

Video Solution

Answer

No

Exercise #1

Is the given graph a function?

–4–4–4–3–3–3–2–2–2–1–1–1111222333444–2–2–2–1–1–1111222000

Video Solution

Answer

Yes

Exercise #2

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 #3

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 #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

Video Solution

Answer

Yes

Exercise #5

Determine whether the following table represents a function

XY02468-3-3-3-3-3

Video Solution

Answer

Yes

Exercise #1

Determine whether the following table represents a function

XY-226101416111621

Video Solution

Answer

Yes

Exercise #2

Determine whether the following table represents a function

XY-1015811

Video Solution

Answer

Yes

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 graph?

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Video Solution

Answer

y=x+4 y=x+4

Exercise #5

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

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

Video Solution

Answer

y=3 y=3

Topics learned in later sections

  1. Ways to represent a function
  2. Graphical Representation of a Function
  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. Interval of decrease of the function
  18. Increasing Intervals of a function
  19. Domain of a Function
  20. Indefinite integral
  21. Inputing Values into a Function