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=2X5 Y=2X-5

Practice 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?

–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. 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. 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