Variation of a Function - Examples, Exercises and Solutions

Question Types:
Variation of a Function: Calculate the rate of change from an equationVariation of a Function: Calculate the rate of change from a tableVariation of a Function: Calculate the rate of change in a graph

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.
Different Types of Rates of Change of a Function

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.

Detailed explanation

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

Question 1

Look at the graph below and determine whether the function's rate of change is constant 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

Question 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

Question 3

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

Question 4

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

Question 5

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

Examples with solutions for Variation of a Function

Exercise #1

Look at the graph below and determine whether the function's rate of change is constant 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

Step-by-Step Solution

First we need to remember that if the function is not a straight line, its rate of change is not constant.

The rate of change is not uniform since the function is not a straight line.

Answer

Not constant

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

Step-by-Step Solution

Let's remember that if the function is not a straight line, its rate of change is not uniform.

Since the graph is not a straight line - the rate of change is not uniform.

Answer

Non-uniform

Exercise #3

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

Video Solution

Step-by-Step Solution

Let's remember that if the function is not a straight line, its rate of change is not uniform.

Since the graph is not a straight line - the rate of change is not uniform.

Answer

Non-uniform

Exercise #4

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

Step-by-Step Solution

Remember that if the function is a straight line, its rate of change will be constant.

Due to the fact that the graph is a straight line - the rate of change is constant.

Answer

Uniform

Exercise #5

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

Question 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

Question 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

Question 3

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

Question 4

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

111222333444555666777888999101010111111121212111222333444555666000

Question 5

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

111222333444555666111222333000

Exercise #6

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 #7

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 #8

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 #9

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

111222333444555666777888999101010111111121212111222333444555666000

Video Solution

Answer

Uniform

Exercise #10

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

111222333444555666111222333000

Video Solution

Answer

Uniform

Question 1

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

Question 2

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

111222333444555666777888999101010111111121212111222333444555666000

Question 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

Question 4

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

XY3579-2-137

Question 5

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

XY-202435812

Exercise #11

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 #12

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

111222333444555666777888999101010111111121212111222333444555666000

Video Solution

Answer

Non-uniform

Exercise #13

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 #14

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

XY3579-2-137

Video Solution

Answer

Non-uniform

Exercise #15

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

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. 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