Question
The graphs below have the same shape. What is the equation of the graph of g(x)?
10本
g(x)
f(x)
5
06800
0★
-10キ
The equation of the graph is
g(x) =x*+2
g(x) = (x+2)2
Answer
# g(x) = (x- 2)3
: g(x) = x'-2
10本
g(x)
f(x)
5
06800
0★
-10キ
The equation of the graph is
g(x) =x*+2
g(x) = (x+2)2
Answer
# g(x) = (x- 2)3
: g(x) = x'-2
Answers
GPT-4o mini
To determine the correct equation for the function \( g(x) \), we first need to analyze the provided options and the relationship between \( f(x) \) and \( g(x) \) based on their shapes.
The choices given are:
1. \( g(x) = x^2 + 2 \)
2. \( g(x) = (x + 2)^2 \)
3. \( g(x) = (x - 2)^3 \)
4. \( g(x) = x^3 - 2 \)
Without the exact visual representation of the graphs, it's important to note the following properties of these equations:
- The equation \( g(x) = x^2 + 2 \) represents a parabola that opens upwards and is shifted up 2 units.
- The equation \( g(x) = (x + 2)^2 \) also represents a parabola that opens upwards but is shifted to the left by 2 units.
- The equation \( g(x) = (x - 2)^3 \) is a cubic function that shifts the graph to the right by 2 units and has a characteristic S-shape.
- The equation \( g(x) = x^3 - 2 \) is another cubic function that shifts the graph down by 2 units.
To conclusively identify the equation, it would be necessary to have either specific points on the graphs or a description of their transformations.
If the graphs of \( f(x) \) and \( g(x) \) are identical except for a shift, or if they indicate a transformation like reflection or rotation, then:
- If they are both parabolas, options 1 and 2 make sense.
- If they resemble cubic functions, options 3 and 4 are more likely.
Choose the option that reflects the transformation characteristics between the two graphs. If you can provide more information about the transformations, I can assist you further in identifying which equation is correct for \( g(x) \).
The choices given are:
1. \( g(x) = x^2 + 2 \)
2. \( g(x) = (x + 2)^2 \)
3. \( g(x) = (x - 2)^3 \)
4. \( g(x) = x^3 - 2 \)
Without the exact visual representation of the graphs, it's important to note the following properties of these equations:
- The equation \( g(x) = x^2 + 2 \) represents a parabola that opens upwards and is shifted up 2 units.
- The equation \( g(x) = (x + 2)^2 \) also represents a parabola that opens upwards but is shifted to the left by 2 units.
- The equation \( g(x) = (x - 2)^3 \) is a cubic function that shifts the graph to the right by 2 units and has a characteristic S-shape.
- The equation \( g(x) = x^3 - 2 \) is another cubic function that shifts the graph down by 2 units.
To conclusively identify the equation, it would be necessary to have either specific points on the graphs or a description of their transformations.
If the graphs of \( f(x) \) and \( g(x) \) are identical except for a shift, or if they indicate a transformation like reflection or rotation, then:
- If they are both parabolas, options 1 and 2 make sense.
- If they resemble cubic functions, options 3 and 4 are more likely.
Choose the option that reflects the transformation characteristics between the two graphs. If you can provide more information about the transformations, I can assist you further in identifying which equation is correct for \( g(x) \).