Variation of a Function - Examples, Exercises and Solutions

Variable Rate of Change

The meaning of a variable rate of change of a function can be seen when the variablesX X change in fixed proportions and the Y Y change unevenly. 

A variable rate of change is represented by a line that is not straight, as seen in the following diagram:

B3 - Function with inconsistent rate of change

Suggested Topics to Practice in Advance

  1. Ways to represent a function
  2. Representing a Function Verbally and with Tables
  3. Graphical Representation of a Function
  4. Algebraic Representation of a Function
  5. Notation of a Function

Practice Variation of a Function

Exercise #1

Given the following graph, determine whether the rate of change is uniform or not

111222333444555666111222333000

Video Solution

Answer

Uniform

Exercise #2

Given the following graph, determine whether the rate of change is uniform or not

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

Video Solution

Answer

Non-uniform

Exercise #3

Given the following graph, determine whether the rate of change is uniform or not

111222333444555666777888999101010111111121212111222333444555666000

Video Solution

Answer

Non-uniform

Exercise #4

Given the following graph, determine whether the rate of change is uniform or not

111222333444555666777888999101010111111121212111222333444555666000

Video Solution

Answer

Uniform

Exercise #5

Given the following graph, determine whether the rate of change is uniform or not

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

Video Solution

Answer

Uniform

Exercise #1

Given the following graph, determine whether the rate of change is uniform or not

–3–3–3–2–2–2–1–1–1111222333444–1–1–1111222333000

Video Solution

Answer

Uniform

Exercise #2

Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Video Solution

Answer

Non-uniform

Exercise #3

Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Video Solution

Answer

Non-uniform

Exercise #4

Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Video Solution

Answer

Non-uniform

Exercise #5

Given the following graph, determine whether the rate of change is uniform or not

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Video Solution

Answer

Non-uniform

Exercise #1

Given the following graph, determine whether function is constant

–9–9–9–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666000

Video Solution

Answer

constant

Exercise #2

Given the following graph, determine whether the rate of change is uniform or not

–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

Uniform

Exercise #3

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

XY-151117381318

Video Solution

Answer

Uniform

Exercise #4

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

XY-202435812

Video Solution

Answer

Non-uniform

Exercise #5

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

XY-2024681012

Video Solution

Answer

Uniform

Topics learned in later sections

  1. Rate of Change of a Function
  2. Variation of a Function
  3. Rate of change represented with steps in the graph of the function
  4. Rate of change of a function represented graphically
  5. Constant Rate of Change
  6. Rate of Change of a Function Represented by a Table of Values
  7. Functions for Seventh Grade
  8. Increasing and Decreasing Intervals (Functions)
  9. Increasing functions
  10. Decreasing function
  11. Constant Function
  12. Decreasing Interval of a function
  13. Increasing Intervals of a function
  14. Domain of a Function
  15. Indefinite integral
  16. Inputing Values into a Function