Use the table to answer the question.

x y
0 −10

10

1 −9

9

2 −8

8

3 −7

7
Using function notation, what is the equation described in the table?(1 point)
f(x)= __x + __

1 answer

To determine the equation described in the table using function notation, we can observe the values of \( x \) and \( y \) to identify a pattern.

The values in the table are:

\[ \begin{align*} y & = -10 \quad \text{when} \quad x = 0 \ y & = -9 \quad \text{when} \quad x = 1 \ y & = -8 \quad \text{when} \quad x = 2 \ y & = -7 \quad \text{when} \quad x = 3 \ \end{align*} \]

From the observations:

  • As \( x \) increases by 1, \( y \) increases by 1.

This indicates a linear relationship with the slope \( m = 1 \).

We also know that when \( x = 0 \), \( y = -10 \). This gives us the \( y \)-intercept \( b = -10 \).

Therefore, we can write the equation in the slope-intercept form \( y = mx + b \) as follows:

\[ y = 1x - 10 \]

In function notation:

\[ f(x) = 1x - 10 \]

Thus, filling in the blanks:

\[ f(x) = 1x + (-10) \]

So, the final answer is:

\[ f(x) = 1x - 10 \]

You can summarize as:

  • The coefficient of \( x \) is 1.
  • The constant is -10.