Variation of a Function - Examples, Exercises and Solutions

Different Types of Rates of Change of a Function

The rate of change of a function describes the pace of modification that the variables Y Y experience with respect to the change in the variables X X .
The rate of change can be:

  • b> b> Constant Rate of Change - fixed
    Describes a situation in which we will see constant intervals of variables Y Y at constant intervals of variables X X .
    In a linear function (a straight line), the rate of change is constant and will be the slope of the function.
  • Non-constant Rate of Change - not fixed
    Describes a situation in which we will see different intervals of variables Y Y at constant intervals of variables X X .
    In a function that is not linear (not a straight line), the rate of change will not be constant. Each part of the function will have a different slope.

We can see the rate of change represented in a graph, a table of values, or by creating steps or stairs in the graph of the function.

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 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

111222333444555666111222333000

Video Solution

Answer

Uniform

Exercise #3

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

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

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 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 #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

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

–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 edge of the function, determine whether the rate of change is uniform or not.

XY-2-1011357

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.

XY12342347

Video Solution

Answer

Non-uniform

Topics learned in later sections

  1. Variation of a Function
  2. Rate of change represented with steps in the graph of the function
  3. Rate of change of a function represented graphically
  4. Constant Rate of Change
  5. Variable 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. Interval of decrease of the function
  13. Increasing Intervals of a function
  14. Domain of a Function
  15. Indefinite integral
  16. Inputing Values into a Function