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

The variation of a function means the rate at which a certain function changes. The rate of variation of a function is also called the slope.

According to the mathematical definition, the slope represents the change of the function (Y) (Y) by increasing the value of X X by 1 1 .

  • If the function's graph is represented by a straight line, it means that the rate of variation of the function is constant
  • However, if the graph is not represented by a straight line, this implies that the rate of variation of the function is not constant
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

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

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

–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 4

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 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

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 #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

–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.

Since the graph is a straight line - the rate of change is constant.

Answer

Uniform

Exercise #4

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 #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

111222333444555666111222333000

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

–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 4

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 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

Exercise #6

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

111222333444555666111222333000

Video Solution

Answer

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

–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 #9

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 #10

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

Question 1

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

111222333444555666777888999101010111111121212111222333444555666000

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.

XY04812-1012

Question 4

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 5

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

XY3579-2-137

Exercise #11

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

111222333444555666777888999101010111111121212111222333444555666000

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.

XY04812-1012

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.

XY-2-1011357

Video Solution

Answer

Uniform

Exercise #15

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

Topics learned in later sections

  1. Rate of Change 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