Question
The graphs below have the same shape. What is the equation of the graph of g(x)?
f(x)
g(x)
>
하
-10本
The equation of the graph is
• Answer
₫ g(x) = (x- 3)?
g(x) =x*-3
::g(x) = x*+3
# g(x) = (x +3)?
f(x)
g(x)
>
하
-10本
The equation of the graph is
• Answer
₫ g(x) = (x- 3)?
g(x) =x*-3
::g(x) = x*+3
# g(x) = (x +3)?
Answers
GPT-4o mini
To determine the equation of the graph \( g(x) \), we need to examine how the graph of \( f(x) \) has been transformed to obtain \( g(x) \). Since I can't see the actual graphs, I'll guide you through a general analysis based on common transformations.
1. **Vertical Shift**: If the graph has been moved up or down, you can add or subtract a constant to the function (e.g. \( g(x) = f(x) + k \)).
2. **Horizontal Shift**: If the graph has been shifted left or right, you adjust the input (e.g. \( g(x) = f(x - h) \) for a right shift of \( h \) units or \( g(x) = f(x + h) \) for a left shift).
3. **Reflection**: If the graph has flipped over the x-axis, multiply the function by -1 (e.g. \( g(x) = -f(x) \)).
4. **Stretch or Compression**: If the graph has been stretched or compressed vertically or horizontally, multiply the function by a constant factor.
Given the answer choices you've provided:
- \( g(x) = (x-3)^2 \)
- \( g(x) = x^2 - 3 \)
- \( g(x) = x^2 + 3 \)
- \( g(x) = (x + 3)^2 \)
Without knowing the specific transformations, I can help you identify which one might be correct based on typical transformations of the graph. You will need to compare the visual characteristics of \( f(x) \) and \( g(x) \).
1. If **\( g(x) \)** looks like a parabola shifted right 3 units, then \( g(x) = (x - 3)^2 \).
2. If **\( g(x) \)** looks like the original parabola shifted down 3 units, then \( g(x) = x^2 - 3 \).
3. If **\( g(x) \)** looks like the original parabola shifted up 3 units, then \( g(x) = x^2 + 3 \).
4. If **\( g(x) \)** looks like a parabola shifted left 3 units, then \( g(x) = (x + 3)^2 \).
Please analyze how \( g(x) \) relates to \( f(x) \) based on their positions and transformations to choose the correct equation.
1. **Vertical Shift**: If the graph has been moved up or down, you can add or subtract a constant to the function (e.g. \( g(x) = f(x) + k \)).
2. **Horizontal Shift**: If the graph has been shifted left or right, you adjust the input (e.g. \( g(x) = f(x - h) \) for a right shift of \( h \) units or \( g(x) = f(x + h) \) for a left shift).
3. **Reflection**: If the graph has flipped over the x-axis, multiply the function by -1 (e.g. \( g(x) = -f(x) \)).
4. **Stretch or Compression**: If the graph has been stretched or compressed vertically or horizontally, multiply the function by a constant factor.
Given the answer choices you've provided:
- \( g(x) = (x-3)^2 \)
- \( g(x) = x^2 - 3 \)
- \( g(x) = x^2 + 3 \)
- \( g(x) = (x + 3)^2 \)
Without knowing the specific transformations, I can help you identify which one might be correct based on typical transformations of the graph. You will need to compare the visual characteristics of \( f(x) \) and \( g(x) \).
1. If **\( g(x) \)** looks like a parabola shifted right 3 units, then \( g(x) = (x - 3)^2 \).
2. If **\( g(x) \)** looks like the original parabola shifted down 3 units, then \( g(x) = x^2 - 3 \).
3. If **\( g(x) \)** looks like the original parabola shifted up 3 units, then \( g(x) = x^2 + 3 \).
4. If **\( g(x) \)** looks like a parabola shifted left 3 units, then \( g(x) = (x + 3)^2 \).
Please analyze how \( g(x) \) relates to \( f(x) \) based on their positions and transformations to choose the correct equation.