Function Representation - Examples, Exercises and Solutions

Ways to represent a function

Algebraic Representation

Representation using an equation of XX and YY

Graphical representation

Representation using a graph, plotting on the XX and YY axis

Tabular representation

Representation using a table X,YX,Y representing points on the graph

Verbal representation

Expressing the relationship between XX and YY using words

Function notation

Y=Y= or f(x)=f(x)=

Practice Function Representation

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?

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–3–3–3–2–2–2–1–1–1111222333444555666000

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. Representing a Function Verbally and with Tables
  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