The image you uploaded contains a mathematical problem written in Croatian, related to linear functions. Here's a translation and breakdown of the task:

Problem:

• For the linear function $f$, it is given that $f(2) = -3$.
• If the value of the variable $x$ increases by 1, the value of the function $f$ decreases by 3.
• Find the function $f$.

Solution:

We are dealing with a linear function, which can be expressed in the general form:

$f(x) = ax + b$

Where $a$ is the slope, and $b$ is the y-intercept.

Step 1: Use the information $f(2) = -3$

Substitute $x = 2$ and $f(2) = -3$ into the general equation:

$f(2) = a(2) + b = -3$

$2a + b = -3 \quad \text{(Equation 1)}$

Step 2: Use the fact that when $x$ increases by 1, $f(x)$ decreases by 3

This means the slope $a$ is -3 because the change in $f(x)$ (the difference in function values) is -3 when $x$ increases by 1.

Therefore, $a = -3$.

Step 3: Solve for $b$

Substitute $a = -3$ into Equation 1:

$2(-3) + b = -3$

$-6 + b = -3$

$b = 3$

Step 4: Write the function

Now we have both $a = -3$ and $b = 3$, so the linear function is:

$f(x) = -3x + 3$

So, the function $f$ is:

$f(x) = -3x + 3$

Would you like any further explanation or have additional questions related to this problem?

Related questions:

1. How would you solve a similar problem where the function changes in a different pattern?
2. What is the geometric interpretation of a linear function in terms of slope and y-intercept?
3. How do you verify the correctness of a linear function using given points?
4. What would happen if the change in function values were different (e.g., an increase in $f(x)$ when $x$ increases)?
5. How would you graph the function $f(x) = -3x + 3$ on the coordinate plane?

Tip: When working with linear functions, always start by using the given points or conditions to first find the slope $a$ and then use a point to find the y-intercept $b$.