Question
Question
Use the table to answer the question.
x y
0 −10
1 −9
2 −8
3 −7 Using function notation, what is the equation described in the table?(1 point)
f(x)=
x+
Use the table to answer the question.
x y
0 −10
1 −9
2 −8
3 −7 Using function notation, what is the equation described in the table?(1 point)
f(x)=
x+
Answers
Answer
theres a number Infront of x
Answer
the - is a +
Answered by
GPT-4o mini
To find the function \( f(x) \) that corresponds to the values in the table, we can observe the relationship between \( x \) and \( y \).
From the table:
- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)
It appears that as \( x \) increases by 1, \( y \) increases by 1 as well. This suggests that the relationship is linear.
To find the function in the form \( f(x) \), we can first identify the slope (the change in \( y \) divided by the change in \( x \)):
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{-9 - (-10)}{1 - 0} = \frac{1}{1} = 1
\]
Since the slope is 1, this implies that the function has the form \( f(x) = x + b \) for some constant \( b \).
To find \( b \), we can use one point from the table. Let's use the first point \( (0, -10) \):
\[
f(0) = 0 + b = -10
\]
Solving for \( b \):
\[
b = -10
\]
Thus, the function can be written as:
\[
f(x) = x - 10
\]
So, the final answer is:
\[
f(x) = x - 10
\]
From the table:
- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)
It appears that as \( x \) increases by 1, \( y \) increases by 1 as well. This suggests that the relationship is linear.
To find the function in the form \( f(x) \), we can first identify the slope (the change in \( y \) divided by the change in \( x \)):
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{-9 - (-10)}{1 - 0} = \frac{1}{1} = 1
\]
Since the slope is 1, this implies that the function has the form \( f(x) = x + b \) for some constant \( b \).
To find \( b \), we can use one point from the table. Let's use the first point \( (0, -10) \):
\[
f(0) = 0 + b = -10
\]
Solving for \( b \):
\[
b = -10
\]
Thus, the function can be written as:
\[
f(x) = x - 10
\]
So, the final answer is:
\[
f(x) = x - 10
\]
Answered by
GPT-4o mini
Thank you for your clarification! Let's revisit the relationship between \( x \) and \( y \) from the table more thoroughly to find a function of the form \( f(x) = mx + b \).
From the table:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & -10 \\
1 & -9 \\
2 & -8 \\
3 & -7 \\
\end{array}
\]
As previously calculated, the difference in \( y \) values as \( x \) increases by 1 is 1. This indicates a slope of \( m = 1 \).
Now, using point \( (0, -10) \):
The general form of a linear function is \( f(x) = mx + b \). Substituting the slope \( m = 1 \) into this, we have:
\[
f(x) = 1 \cdot x + b = x + b
\]
To find \( b \), we'll use the point \( (0, -10) \):
\[
f(0) = 0 + b = -10
\]
\[
b = -10
\]
Therefore, our function so far is:
\[
f(x) = x - 10
\]
If you're looking for a form with a coefficient in front of \( x \) (which could be represented as a number beside \( x \)), then we have:
\[
f(x) = 1x - 10
\]
So the equation you're looking for, in function notation, is:
\[
f(x) = 1x - 10
\]
or simply:
\[
f(x) = x - 10
\]
if you prefer. However, if you strictly want to see the coefficient explicitly, it can be shown as \( 1x - 10 \).
From the table:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & -10 \\
1 & -9 \\
2 & -8 \\
3 & -7 \\
\end{array}
\]
As previously calculated, the difference in \( y \) values as \( x \) increases by 1 is 1. This indicates a slope of \( m = 1 \).
Now, using point \( (0, -10) \):
The general form of a linear function is \( f(x) = mx + b \). Substituting the slope \( m = 1 \) into this, we have:
\[
f(x) = 1 \cdot x + b = x + b
\]
To find \( b \), we'll use the point \( (0, -10) \):
\[
f(0) = 0 + b = -10
\]
\[
b = -10
\]
Therefore, our function so far is:
\[
f(x) = x - 10
\]
If you're looking for a form with a coefficient in front of \( x \) (which could be represented as a number beside \( x \)), then we have:
\[
f(x) = 1x - 10
\]
So the equation you're looking for, in function notation, is:
\[
f(x) = 1x - 10
\]
or simply:
\[
f(x) = x - 10
\]
if you prefer. However, if you strictly want to see the coefficient explicitly, it can be shown as \( 1x - 10 \).
Answered by
GPT-4o mini
Thank you for your patience and clarification. Let's update the analysis accordingly.
From the original table:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & -10 \\
1 & -9 \\
2 & -8 \\
3 & -7 \\
\end{array}
\]
Since you're indicating that the relationship might be positive, let's look again at the sequence of values.
As \( x \) increases by 1, \( y \) increases by 1:
- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)
This means that the relationship can be represented as:
\[
y = x - 10
\]
In function notation, this means:
\[
f(x) = x - 10
\]
Based on your prompt, if we are to change the minus to a plus, I understand that you want to express \( y \) as an increasing function.
If you're looking for something like \( f(x) = kx + b \) where \( k \) is a positive number:
Given the values, we can express \( f(x) \) more appropriately recognizing:
The resulting points lead to a consistent pattern if we adjust how we see the equation as a transformation.
To make the final adjustment based on your message, let's express the function as:
\[
f(x) = 1x + (-10)
\]
or simplified:
\[
f(x) = x + (-10) \quad \text{(where the '-' indicates moving down)}
\]
So directly denoting shifted relationships back based on your note, the correct function is still \( f(x) = x - 10 \), but to denote you want to see directly "+":
Ultimately:
\[
f(x) = x + (-10)
\]
This capturing of the form keeps it leading towards increasing but centered correctly on values presented and connecting accordingly. If you would like further adjustments, please specify again! Thank you!
From the original table:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & -10 \\
1 & -9 \\
2 & -8 \\
3 & -7 \\
\end{array}
\]
Since you're indicating that the relationship might be positive, let's look again at the sequence of values.
As \( x \) increases by 1, \( y \) increases by 1:
- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)
This means that the relationship can be represented as:
\[
y = x - 10
\]
In function notation, this means:
\[
f(x) = x - 10
\]
Based on your prompt, if we are to change the minus to a plus, I understand that you want to express \( y \) as an increasing function.
If you're looking for something like \( f(x) = kx + b \) where \( k \) is a positive number:
Given the values, we can express \( f(x) \) more appropriately recognizing:
The resulting points lead to a consistent pattern if we adjust how we see the equation as a transformation.
To make the final adjustment based on your message, let's express the function as:
\[
f(x) = 1x + (-10)
\]
or simplified:
\[
f(x) = x + (-10) \quad \text{(where the '-' indicates moving down)}
\]
So directly denoting shifted relationships back based on your note, the correct function is still \( f(x) = x - 10 \), but to denote you want to see directly "+":
Ultimately:
\[
f(x) = x + (-10)
\]
This capturing of the form keeps it leading towards increasing but centered correctly on values presented and connecting accordingly. If you would like further adjustments, please specify again! Thank you!
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