Question
Given the graph of the function f(x), complete the following table of the points for the horizontal reflected function f(-x)
x -1 -2 -3
f(-x)
x -1 -2 -3
f(-x)
Answers
GPT-4o mini
To find the values of the function \( f(-x) \), you will need to determine the corresponding values of \( f(x) \) at \( -x \) for the values provided in the table. This involves reflecting the original points of \( f(x) \) across the y-axis.
Here's how you can complete the table step by step for \( x = -1, -2, -3 \):
1. For \( x = -1 \):
- Calculate \( f(-(-1)) = f(1) \).
- Find the value of \( f(1) \) using the graph of \( f(x) \).
2. For \( x = -2 \):
- Calculate \( f(-(-2)) = f(2) \).
- Find the value of \( f(2) \) using the graph of \( f(x) \).
3. For \( x = -3 \):
- Calculate \( f(-(-3)) = f(3) \).
- Find the value of \( f(3) \) using the graph of \( f(x) \).
After finding the values \( f(1) \), \( f(2) \), and \( f(3) \), you can place them into the corresponding spots in the table for \( f(-x) \).
Since I don't have access to the graph of the function \( f(x) \), I cannot give you the specific values. Please refer to the graph to identify \( f(1) \), \( f(2) \), and \( f(3) \) and fill out the table accordingly. If you provide those function values, I could help you to complete your table!
Here's how you can complete the table step by step for \( x = -1, -2, -3 \):
1. For \( x = -1 \):
- Calculate \( f(-(-1)) = f(1) \).
- Find the value of \( f(1) \) using the graph of \( f(x) \).
2. For \( x = -2 \):
- Calculate \( f(-(-2)) = f(2) \).
- Find the value of \( f(2) \) using the graph of \( f(x) \).
3. For \( x = -3 \):
- Calculate \( f(-(-3)) = f(3) \).
- Find the value of \( f(3) \) using the graph of \( f(x) \).
After finding the values \( f(1) \), \( f(2) \), and \( f(3) \), you can place them into the corresponding spots in the table for \( f(-x) \).
Since I don't have access to the graph of the function \( f(x) \), I cannot give you the specific values. Please refer to the graph to identify \( f(1) \), \( f(2) \), and \( f(3) \) and fill out the table accordingly. If you provide those function values, I could help you to complete your table!
The graph is downward u shape in the quadrant 4 with the curve at 2 on x axis
GPT-4o mini
Given the description of the graph as a downward U-shape that is located in the fourth quadrant and touches the x-axis at \( x = 2 \), we can infer that the function likely has a minimum point at that location, indicating it is a parabolic function.
From this, we can assume that the function might resemble:
\[ f(x) = -(x - 2)^2 + k \]
Where \( k \) is some constant that places the vertex of the parabola in the fourth quadrant.
### Finding Values for \( f(-x) \)
Let's assume the vertex of the parabola is at \( (2, 0) \) based on your description. Thus, we can suggest a standard form for illustration purposes:
Assuming \( f(x) = - (x-2)^2 \), then:
- The minimum point (vertex) is at \( (2, 0) \).
- The parabola opens downwards.
Now let's calculate the points for \( f(-x) \) at \( x = -1, -2, -3 \):
1. **For \( x = -1\):**
- \( f(-(-1)) = f(1) = - (1 - 2)^2 = - (1)^2 = -1 \)
2. **For \( x = -2\):**
- \( f(-(-2)) = f(2) = - (2 - 2)^2 = - (0)^2 = 0 \)
3. **For \( x = -3\):**
- \( f(-(-3)) = f(3) = - (3 - 2)^2 = - (1)^2 = -1 \)
### Completing the Table
Thus, we can complete the table for \( f(-x) \):
\[
\begin{array}{|c|c|}
\hline
x & f(-x) \\
\hline
-1 & -1 \\
-2 & 0 \\
-3 & -1 \\
\hline
\end{array}
\]
If the actual function differs, please provide more details or a different specification, and I can adjust the calculations accordingly!
From this, we can assume that the function might resemble:
\[ f(x) = -(x - 2)^2 + k \]
Where \( k \) is some constant that places the vertex of the parabola in the fourth quadrant.
### Finding Values for \( f(-x) \)
Let's assume the vertex of the parabola is at \( (2, 0) \) based on your description. Thus, we can suggest a standard form for illustration purposes:
Assuming \( f(x) = - (x-2)^2 \), then:
- The minimum point (vertex) is at \( (2, 0) \).
- The parabola opens downwards.
Now let's calculate the points for \( f(-x) \) at \( x = -1, -2, -3 \):
1. **For \( x = -1\):**
- \( f(-(-1)) = f(1) = - (1 - 2)^2 = - (1)^2 = -1 \)
2. **For \( x = -2\):**
- \( f(-(-2)) = f(2) = - (2 - 2)^2 = - (0)^2 = 0 \)
3. **For \( x = -3\):**
- \( f(-(-3)) = f(3) = - (3 - 2)^2 = - (1)^2 = -1 \)
### Completing the Table
Thus, we can complete the table for \( f(-x) \):
\[
\begin{array}{|c|c|}
\hline
x & f(-x) \\
\hline
-1 & -1 \\
-2 & 0 \\
-3 & -1 \\
\hline
\end{array}
\]
If the actual function differs, please provide more details or a different specification, and I can adjust the calculations accordingly!