# linear function

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?

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

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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 $-8\le y\le 10$.

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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

f(2)= 3 times 2 − 2

f(-1)= 3 times -1 - 2

and so on because the -1 in f(-1) is the x-value and if that is the x-value then the the equation 3x-2 it would end up as 3 times -1 subtracted by 2. Which will end up with: 3 times -1=-3 -3 subtracted by 2=-5 So the answer for f(-1) is equal to -5. I hope that this helps even though this was a post form 2 years ago...

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For some basic information about writing math at this site see e.g. here, here, here and here. – Bye_World Jan 11 '15 at 17:35
Oh, I never knew that, thanks. – Yeujer Jan 12 '15 at 0:15