Question
6.
Given the graph of a function with multiple translations, write the new function rule for the translated graph.
(1 point)
The graphs below shows g(x)
, which is a translation of f(x)=x2
. Write the function rule for g(x)
. Write your answer in the form a(x−h)2+k
. Remember to use another point to solve for a
.
#1 g(x)=
Question 2
7.
The original function contains the point (10, 32) and is translated to a new function, where the original point is mapped to (5, 32). Which of the following best describes the translation in the graph?
(1 point)
Responses
The function is translated 5 units to the right and has the same slope
The function is translated 5 units to the right and has the same slope
The function is translated 5 units to the right and has a larger slope
The function is translated 5 units to the right and has a larger slope
The function is translated 5 units to the left and has a larger slope
The function is translated 5 units to the left and has a larger slope
The function is translated 5 units to the left and has the same slope
Given the graph of a function with multiple translations, write the new function rule for the translated graph.
(1 point)
The graphs below shows g(x)
, which is a translation of f(x)=x2
. Write the function rule for g(x)
. Write your answer in the form a(x−h)2+k
. Remember to use another point to solve for a
.
#1 g(x)=
Question 2
7.
The original function contains the point (10, 32) and is translated to a new function, where the original point is mapped to (5, 32). Which of the following best describes the translation in the graph?
(1 point)
Responses
The function is translated 5 units to the right and has the same slope
The function is translated 5 units to the right and has the same slope
The function is translated 5 units to the right and has a larger slope
The function is translated 5 units to the right and has a larger slope
The function is translated 5 units to the left and has a larger slope
The function is translated 5 units to the left and has a larger slope
The function is translated 5 units to the left and has the same slope
Answers
GPT-4o mini
### Question 1
To write the function rule for \( g(x) \), we start from \( f(x) = x^2 \).
Assuming \( g(x) \) is a translation of \( f(x) \) in the form \( g(x) = a(x - h)^2 + k \), we need to identify the values of \( a \), \( h \), and \( k \).
1. **Identify Translation:**
- Determine the value of \( h \) and \( k \) by looking at how the graph of \( f(x) \) is transformed to get \( g(x) \).
- If the graph shifts to the left or right, \( h \) will be negative or positive respectively.
- If the graph shifts up or down, \( k \) will be positive or negative respectively.
2. **Find the Point for Scaling \( a \):**
- Use another point on the graph of \( g(x) \) (besides any provided) to determine \( a \).
- Substitute the coordinates of that point into the equation \( g(x) = a(x - h)^2 + k \) and solve for \( a \).
Without explicit values from a graph, I can't provide the exact function for \( g(x) \). If you provide specific points or transformations observed, I can assist with the calculations.
### Question 2
The original function has the point (10, 32) and translates to (5, 32).
1. **Change in X-Coordinate:**
- \( 10 \) to \( 5 \) is a shift to the **left** by \( 5 \) units.
2. **Change in Y-Coordinate:**
- The y-coordinate remains constant at \( 32 \), meaning the slope and vertical position of points on the graph do not change, confirming that the slope remains the **same**.
### Conclusion:
The correct description of the translation is:
**The function is translated 5 units to the left and has the same slope.**
To write the function rule for \( g(x) \), we start from \( f(x) = x^2 \).
Assuming \( g(x) \) is a translation of \( f(x) \) in the form \( g(x) = a(x - h)^2 + k \), we need to identify the values of \( a \), \( h \), and \( k \).
1. **Identify Translation:**
- Determine the value of \( h \) and \( k \) by looking at how the graph of \( f(x) \) is transformed to get \( g(x) \).
- If the graph shifts to the left or right, \( h \) will be negative or positive respectively.
- If the graph shifts up or down, \( k \) will be positive or negative respectively.
2. **Find the Point for Scaling \( a \):**
- Use another point on the graph of \( g(x) \) (besides any provided) to determine \( a \).
- Substitute the coordinates of that point into the equation \( g(x) = a(x - h)^2 + k \) and solve for \( a \).
Without explicit values from a graph, I can't provide the exact function for \( g(x) \). If you provide specific points or transformations observed, I can assist with the calculations.
### Question 2
The original function has the point (10, 32) and translates to (5, 32).
1. **Change in X-Coordinate:**
- \( 10 \) to \( 5 \) is a shift to the **left** by \( 5 \) units.
2. **Change in Y-Coordinate:**
- The y-coordinate remains constant at \( 32 \), meaning the slope and vertical position of points on the graph do not change, confirming that the slope remains the **same**.
### Conclusion:
The correct description of the translation is:
**The function is translated 5 units to the left and has the same slope.**