Algebraic Representation of a Function - Examples, Exercises and Solutions

A function is a connection between an independent variable (X) (X) and a dependent variable (Y) (Y) . The relationship between the variables is called a "correspondence rule".

An algebraic representation of a function is actually a description of the relationship between the dependent variable (Y) (Y) and the independent variable (X) (X) by means of an equation.

The following is the typical structure of a graphical representation:

  • Y=X+3 Y=X+3 , Y=2X−5 Y=2X-5

For example, if the data is that every month, Daniel earns20.000 20.000 dollars.

The algebraic representation will be X X for the number of months Y Y f(X) f (X) for the amount earned. f(x)=20000X f (x) = 20000X

A1 - algebraic representation of a function

Detailed explanation

Practice Algebraic Representation of a Function

Question 1

Is the given graph a function?

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Question 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

Question 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

Question 4

Determine whether the following table represents a function

XY-1015811

Question 5

Determine whether the following table represents a function

XY02468-3-3-3-3-3

examples with solutions for algebraic representation of a function

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?

–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

Yes

Exercise #4

Determine whether the following table represents a function

XY-1015811

Video Solution

Answer

Yes

Exercise #5

Determine whether the following table represents a function

XY02468-3-3-3-3-3

Video Solution

Answer

Yes

Question 1

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

XY012348

Question 2

Determine whether the following table represents a function

XY-101247

Question 3

Determine whether the following table represents a function

XY-226101416111621

Question 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

Question 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

examples with solutions for algebraic representation of a function

Exercise #1

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

XY012348

Video Solution

Answer

No

Exercise #2

Determine whether the following table represents a function

XY-101247

Video Solution

Answer

No

Exercise #3

Determine whether the following table represents a function

XY-226101416111621

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

No

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

Video Solution

Answer

Yes

Question 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

Question 2

Is the given graph a function?

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

Question 3

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

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Question 4

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

XY-3-1135246810

Question 5

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

XY-125811246810

examples with solutions for algebraic representation of a function

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

No

Exercise #2

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 #3

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

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Video Solution

Answer

y=−x−2 y=-x-2

Exercise #4

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

XY-3-1135246810

Video Solution

Answer

y=x+5 y=x+5

Exercise #5

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

XY-125811246810

Video Solution

Answer

y=23x+223 y=\frac{2}{3}x+2\frac{2}{3}

Topics learned in later sections

  1. Ways to represent a function
  2. Representing a Function Verbally and with Tables
  3. Graphical 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