Variation of a Function

🏆Practice variation of a function

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
Start practice

Test yourself on variation of a function!

einstein

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

111222333444555666111222333000

Practice more now

That is, there are functions, such as the linear function (which we will study in more detail later, but generally speaking, it is a function with the variable to the first power) in which the slope, or in other words, the rate of change of the function is constant, and there are other functions that may have an increasing or decreasing rate of change that is calculated separately for each value X X .

A1 - function_rate_of_change_image.

Exercises on the variation of a function

Exercise 1

Assignment

y=5x2+x y=-5x^{2}+x

Solution

a a coefficient of x2 x^2

Given in the exercise: 5 -5

b b coefficient of x x

Given in the exercise: 1 1

c c is a free number

Therefore it is: 0 0

Answer

a=5, b=1, c=0 a=-5,~b=1,~c=0


Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge

Exercise 2

Assignment

Given the linear function in the graph

When is the function positive?

Exercise 2 - Given the linear function in the graph

Solution

The function is positive when it is above the axis: x x

Pay attention that the intersection point with the axis x x is (2,0) \left(2,0\right)

According to the graph, the function is positive, therefore x>2 x\gt2

Answer

x>2 x\gt2


Exercise 3

Assignment

Given the function in the graph

When is the function positive?

When is the function positive

Solution

The intersection point with the axis :x x is: (4,0) \left(-4,0\right)

First positive, then negative.

Therefore x<4 x<-4

Answer

x<4 x<-4


Do you know what the answer is?

Exercise 4

Assignment

y=40x+40 y=-40x+40

Solution

a a coefficient of x2 x^2

Given in the exercise: 0 0

b b coefficient of x x

Given in the exercise: 40 -40

c c is a free number

Therefore it is: 40 40

Answer

a=0, b=40, c=40 a=0,~b=-40,~c=40


Exercise 5

Assignment

y=x2+3x+40 y=-x^{2}+3x+40

Solution

a a coefficient of x2 x^2

Given in the exercise: 1 -1

b b coefficient of x x

Given in the exercise: 3 3

c c is a free number

Therefore it is: 40 40

Answer

a=1, b=3, c=40 a=-1,~b=3,~c=40


Check your understanding

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

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 #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.

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

Answer

Uniform

Exercise #5

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

111222333444555666111222333000

Video Solution

Answer

Uniform

Start practice