Rate of Change Function Practice Problems & Solutions

Master constant and non-constant rates of change with step-by-step practice problems. Learn graphical, table, and step methods with detailed solutions.

📚Master Rate of Change Through Interactive Practice
  • Identify constant vs non-constant rates of change from graphs and tables
  • Calculate slopes and rates of change for linear and non-linear functions
  • Interpret rate of change using step diagrams on function graphs
  • Analyze value tables to determine if rate of change is fixed or variable
  • Connect rate of change concepts to real-world slope applications
  • Practice identifying rates of change in y = mx + b format functions

Understanding Variation of a Function

Complete explanation with examples

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

Practice Variation of a Function

Test your knowledge with 9 quizzes

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

XY04812-1012

Examples with solutions for Variation of a Function

Step-by-step solutions included
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

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

Video Solution
Exercise #2

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

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

Video Solution
Exercise #3

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

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

Video Solution
Exercise #4

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

Step-by-Step Solution

The problem requires us to determine whether the rate of change in a given graph is uniform.

A uniform rate of change corresponds to a constant slope, which is characteristic of a linear graph. First, we'll examine the graphical representation.

Upon observing the graph, we see that it displays a straight horizontal line. A horizontal line on a graph indicates that for any two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), the difference in yy-values is zero, i.e., y2−y1=0y_2 - y_1 = 0. This implies that the slope, given by the formula y2−y1x2−x1 \frac{y_2 - y_1}{x_2 - x_1} , is zero and remains constant as we move along the line.

Because the line is horizontal and does not change its slope throughout, the rate of change is indeed uniform across the entire graph.

Therefore, the rate of change is uniform.

Answer:

Uniform

Video Solution
Exercise #5

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

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

Video Solution

Frequently Asked Questions

Everything you need to know about Variation of a Function

What is the rate of change of a function?

+
The rate of change describes how quickly the Y variable changes with respect to changes in the X variable. For linear functions, this is the slope and remains constant throughout the function.

How do you know if a function has constant rate of change?

+
A function has constant rate of change if: 1) Its graph is a straight line, 2) In a value table, Y changes by the same amount for equal X intervals, 3) The function is linear (y = mx + b format).

What's the difference between constant and non-constant rate of change?

+
Constant rate of change means Y changes by the same amount for equal X intervals (straight line graph). Non-constant rate of change means Y changes by different amounts for equal X intervals (curved graph).

How do you find rate of change from a table of values?

+
Choose equal intervals for X values, then calculate how much Y changes for each interval. If Y changes by the same amount each time, the rate is constant. If Y changes by different amounts, the rate is non-constant.

What does rate of change look like on a graph?

+
Constant rate of change appears as a straight line with consistent slope. Non-constant rate of change appears as a curved line where the steepness varies at different points.

How do step diagrams show rate of change?

+
Step diagrams use rectangular 'steps' where the base represents the X interval and the height represents the Y interval. Equal-sized steps indicate constant rate of change, while varying step sizes show non-constant rate.

Is rate of change the same as slope?

+
For linear functions, yes - the rate of change equals the slope (m in y = mx + b). For non-linear functions, the rate of change varies, so different parts have different slopes.

Why is rate of change important in math?

+
Rate of change helps describe how quantities change in real situations like speed, growth rates, and trends. It's fundamental for understanding functions, calculus, and modeling real-world relationships.

More Variation of a Function Questions

Click on any question to see the complete solution with step-by-step explanations

Variation of a Function

Find the Rate of Change: Solving -x+y=0 Linear Equation Find the Rate of Change in the Linear Equation: -5x+y=3 Find the Rate of Change in the Linear Equation 3-y=1/4x Find the Rate of Change in Linear Equation -8y+2x=6 Find the Rate of Change: Solving -1/4y + x = 3

Continue Your Math Journey

Master Variation of a Function first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

Ways to Represent a FunctionRepresenting a Function Verbally and with TablesGraphical Representation of a FunctionAlgebraic Representation of a FunctionNotation of a Function

Topics Learned in Later Sections

Variation of a FunctionRate of change represented with steps in the graph of the functionRate of change of a function represented graphicallyConstant Rate of ChangeVariable Rate of ChangeRate of Change of a Function Represented by a Table of ValuesFunctions for Seventh GradeIncreasing and Decreasing Intervals (Functions)Increasing functionsDecreasing functionConstant FunctionDecreasing Interval of a functionIncreasing Intervals of a functionDomain of a FunctionIndefinite integralInputing Values into a Function

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems
Calculate the rate of change from an equation Drawing conclusions from a table or graph Calculate the rate of change from a table Calculate the rate of change in a graph