Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I don't get this, need some help, examples and information

The linear function $f$ is given by $$f(x) = 3x - 2 ,\quad -2 \leq x \leq 4.$$

  1. Enter the independent variable and the dependent variable.

  2. Determine the function values ​$​f (-2)$, $f (-1)$, $f (0)$ and $f (4)$.

Enter the definitions and values ​​crowd.

I know what a function is, but how can you find the independent variable and the dependent variable?

How one can determines the function values ​​and how you specify the definitions and values ​​crowd?

What I know about functions:

Variables can have any name, $x$, $y$, $z$, or "maria", "girl", "young"; at a specific value and function can be called anything.

My own example of functions:

Age = 18

year = 6

Maria (age, years) = age + years = 24

in 6 years Maria is going be 24 years

share|improve this question

1 Answer 1

up vote 4 down vote accepted

The independent variable is $x$. The dependent "variable" is probably intended to be $f(x)$. This is a somewhat unusual use of language. It is used more often when write the relationship as $y=3x-2$. Then $y$ is called the dependent variable. In modern mathematics, the terms "independent variable" and "dependent variable" are used much less than in the past.

For the calculations, we answer a question that wasn't asked: What is $f(0.5)$? Well, $f(0.5)=3(0.5)-2=-0.5$. We just plug in $0.5$ everywhere that we see $x$, and then calculate. Similar calculations will deal with the questions of this type that you were asked.

The "definitions crowd" is the set of all numbers at which the function is defined. You were told in the problem what this set is. It is the set of all real numbers $x$ such that $-2\le x\le 4$. In English, this is usually called the domain (of definition) of the function.

What you call the "values crowd" is usually called in English the range of the function. It is the set of all values that $f(x)$ can take on as $x$ takes on all possible values in the domain of definition.

Note that $f(-2)=3(-2)-2=-8$, and that $f(4)=3(4)-2=10$. It is probably clear that as $x$ travels from $-2$ to $4$, $f(x)$ steadily increases from $-8$ to $10$. So the range of the function is the set of all real numbers $y$ such that $-8\le y\le 10$.

share|improve this answer
    
So: -2 ≤ x ≤ 4 is: Dm(f) = [-2 ; 4 ] , which means the range is from -2 to 4. But how do i know what x is and what y is ? is it (−8, 10 ), so i can draw it ? –  user1022734 Feb 7 '12 at 21:29
    
The range is from $-8$ to $10$, in your wording and notation the crowd of values is $[-8;10]$. To draw it pick any two points on the line, join them. For example, when $x=-2$, $y=-8$, and when $x=4$, $y=10$. So on graph paper, make a dot at $(-2,-8)$, another at $(4,10)$, and join the two dots by a line segment. –  André Nicolas Feb 7 '12 at 21:48
    
If a line having slope 3 and passes through points (3,4) and (5, y). how can you one determines y? –  user1022734 Feb 7 '12 at 22:00
    
Change in $y$-coordinate divided by change in $x$-coordinate is the slope. The change in the $y$-coordinate is $y-4$. The change in the $x$-coordinate is $5-3$, which is $2$. So $\frac{y-4}{2}=3$. Now solve for $y$. –  André Nicolas Feb 7 '12 at 22:05
    
I don't really get it, but can you please describe more? –  user1022734 Feb 7 '12 at 22:14

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.