On one hand, functions are a fairly abstract concept, but on the other hand, they are very useful in many areas of mathematics. The topic of functions dominates many fields, including algebra, trigonometry, differential and integral calculus, and more. Therefore, it's important to understand the concept of functions, so that it can be applied in any of the fields of mathematics, and especially when we start learning about functions in seventh grade.
A function expresses a relationship between two variables (X and Y)
An independent variable is a non-variable constant by which we explain , the dependent variable
For example, if Daniela worked as a babysitter and earned 30 dollars per hour and we want to know how much Daniela made after hours, the number of hours worked is actually the independent variable with which we know how much she earned. Ultimately this is the dependent variable.
In other words, it can be said that the amount Daniela earned is a function of the number of hours she worked .
We will mark the data of the function algebraically in this way:
It's important to remember that each element in the domain will always have only one element in the range .
This means that it's not possible that during the hours Daniela worked, she received both dollars and dollars.
Determine which domain corresponds to the function described below:
The function represents the amount of fuel in a car's tank according to the distance traveled by the car.
Choose the graph that best describes the following:
The acceleration of a ball (Y) after throwing it from a building as a function of time (X).
Choose the graph that best represents the following:
Temperature of lukewarm water (Y) after placing in the freezer as a function of time (X).
Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.
For each number, multiply by\( (-1) \).
Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.
For each number, multiply by 0.
Determine which domain corresponds to the function described below:
The function represents the amount of fuel in a car's tank according to the distance traveled by the car.
According to the definition, the amount of fuel in the car's tank will always decrease, since during the trip the car consumes fuel in order to travel.
Therefore, the domain that is suitable for this function is - always decreasing.
Always decreasing
Choose the graph that best describes the following:
The acceleration of a ball (Y) after throwing it from a building as a function of time (X).
Since acceleration is dependent on time, it will be constant.
The force of gravity on Earth is constant, meaning the velocity of Earth's gravity is constant and therefore the graph will be straight.
The graph that appears in answer B satisfies this.
Choose the graph that best represents the following:
Temperature of lukewarm water (Y) after placing in the freezer as a function of time (X).
Since the freezing point of water is below 0, the temperature of the water must drop below 0.
The graph in answer B describes a decreasing function and therefore this is the correct answer.
Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.
For each number, multiply by.
The function is:
Let's start by assuming that x equals 0:
Now let's assume that x equals minus 1:
Now let's assume that x equals 1:
Now let's assume that x equals 2:
Let's plot all the points on the function graph:
We can see that the function we got is a decreasing function.
Decreasing
Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.
For each number, multiply by 0.
The function is:
Let's start by assuming that x equals 0:
Now let's assume that x equals 1:
Now let's assume that x equals -1:
Now let's assume that x equals 2:
Let's plot all the points on the function's graph:
We can see that the function we obtained is a constant function.
Constant
Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table:
Each number is divided by \( (-1) \).
In what domain does the function increase?
In what domain is the function negative?
In what domain is the function increasing?
In what domain does the function increase?
Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table:
Each number is divided by .
The function is:
Let's start by assuming that x equals 0:
Now let's assume that x equals 1:
Now let's assume that x equals 2:
Let's plot all the points on the function graph:
We see that we got a decreasing function.
Decreasing
In what domain does the function increase?
x > 0
In what domain is the function negative?
x > 1
In what domain is the function increasing?
Entire
In what domain does the function increase?
x<0
In what interval is the function increasing?
Purple line: \( x=0.6 \)
In what domain does the function increase?
Green line:
\( x=-0.8 \)
In which interval does the function decrease?
Red line: \( x=0.65 \)
In which interval does the function decrease?
Red line: \( x=1.3 \)
In what domain does the function increase?
Black line: \( x=1.1 \)
In what interval is the function increasing?
Purple line:
x<0.6
In what domain does the function increase?
Green line:
All values of
In which interval does the function decrease?
Red line:
All values of
In which interval does the function decrease?
Red line:
1.3 > x > -1.3
In what domain does the function increase?
Black line:
1.1 > x > 0