Rate of change represented with steps in the graph of the 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

Rate of change represented by steps in the function graph

We can draw stairs on the graph of the function to see the rate of change.
The base of the step will represent the interval in the X X variables and the height will symbolize the interval in the Y Y .

The step will mark the "jump" from X X in relation to the "jump" in Y Y .
The bases of the steps will always be the same since we always choose fixed intervals in X X .

  • If the heights of the steps are increasing, it means that the rate of change is increasing.
  • If the heights of the steps are decreasing, it means that the rate of change is decreasing.
  • If the heights of the steps do not change, it means that the rate of change is constant.
Rate of change represented by steps in the function graph

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 Rate of change represented with steps in the graph of the 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 Rate of change represented with steps in the graph of the 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. Variation of a 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