Question

Answer the questions below to determine what kind of function is depicted in the table below. xx 00 11 22 33 44 f, of, xf(x) minus, 1−1 minus, 7−7 minus, 13−13 minus, 19−19 minus, 25−25

Answer 1

To determine the nature of the function depicted in the table, let's first outline the information you've provided more clearly:

Given \( x \) values:
- \( 0, 1, 2, 3, 4 \)

Given \( f(x) \) values:
- \( -1, -7, -13, -19, -25 \)

Now, we can examine the relationship between the \( x \) values and the \( f(x) \) values.

1. **Identifying the Change in \( f(x) \)**:
Calculate the differences of \( f(x) \):
- From \( -1 \) to \( -7 \): \( -7 - (-1) = -6 \)
- From \( -7 \) to \( -13 \): \( -13 - (-7) = -6 \)
- From \( -13 \) to \( -19 \): \( -19 - (-13) = -6 \)
- From \( -19 \) to \( -25 \): \( -25 - (-19) = -6 \)

The difference is consistently \( -6 \), suggesting that the function is linear.

2. **Finding Function Equation**:
Since it's linear, we can express the function in the form \( f(x) = mx + b \).

Using the first point \( (0, -1) \):
\[
f(0) = -1 \Rightarrow b = -1
\]
Now, we use the slope, calculated from the change:
- The slope \( m \) is \( -6 \).

Thus, we can write:
\[
f(x) = -6x - 1
\]

### Conclusion:
The function represented by the table is a linear function, specifically \( f(x) = -6x - 1 \).