[ f_(1)(x)=a x+b ] 8 x : Seja a Tabela x & -1 & 0 & 1 & 2 F(x) & 4 & 2 & 1 & 5 Qivando vale F(0,25)= ? [ P(x i)=F(x i) ]

## Step 1: Understand the Problem
### We are given a table with values of $x$ and corresponding function values $F(x)$. The function $f_1(x) = ax + b$ is linear, and we need to determine its coefficients $a$ and $b$ using the provided data points. Then, we will use this function to find $F(0.25)$.

## Step 2: Set Up Equations Using Known Points
### From the table, we have the following pairs:
- $(-1, 4)$
- $(0, 2)$
- $(1, 1)$
- $(2, 5)$

### We can use any two points to find the coefficients $a$ and $b$. Let's use the points $(0, 2)$ and $(1, 1)$.

## Step 3: Calculate the Slope $a$
### The slope $a$ of the line can be calculated using the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$:
$$a = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 2}{1 - 0} = -1$$

## Step 4: Determine the Intercept $b$
### Using the point $(0, 2)$, where $x = 0$ and $f_1(x) = 2$, we substitute into the equation:
$$f_1(x) = ax + b \Rightarrow 2 = -1 \cdot 0 + b \Rightarrow b = 2$$

## Step 5: Formulate the Function
### Now that we have $a = -1$ and $b = 2$, the function becomes:
$$f_1(x) = -x + 2$$

## Step 6: Calculate $F(0.25)$
### Substitute $x = 0.25$ into the function:
$$F(0.25) = -0.25 + 2 = 1.75$$