Question
On a coordinate plane, a red curved line with an upward arc, labeled g of x, crosses the x-axis at (negative 2, 0), and the y-axis at (0, 4). A blue curved line with an upward arc, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which statement is true regarding the graphed functions?
Which statement is true regarding the graphed functions?
Answers
GPT-4o mini
To analyze the two functions \( g(x) \) and \( f(x) \) based on the given information, we note the following:
1. **Function \( g(x) \)**:
- Crosses the x-axis at \((-2, 0)\): This means that \( g(-2) = 0 \).
- Crosses the y-axis at \((0, 4)\): This means that \( g(0) = 4 \).
2. **Function \( f(x) \)**:
- Crosses the x-axis at \((2, 0)\): This means that \( f(2) = 0 \).
- Crosses the y-axis at \((0, 4)\): This means that \( f(0) = 4 \).
From this information, we can draw a few conclusions about the functions:
- Both \( g(x) \) and \( f(x) \) have the same y-intercept at \( (0, 4) \).
- \( g(x) \) has an x-intercept at \( x = -2 \), while \( f(x) \) has an x-intercept at \( x = 2 \).
- Since both functions are upward arcs, it can be inferred that they are both parabolic functions, but they open in different directions horizontally with respect to the x-axis.
In summary, the true statement regarding the graphed functions is that they share the same y-intercept but cross the x-axis at different points: \( g(x) \) at \( x = -2 \) and \( f(x) \) at \( x = 2 \).
1. **Function \( g(x) \)**:
- Crosses the x-axis at \((-2, 0)\): This means that \( g(-2) = 0 \).
- Crosses the y-axis at \((0, 4)\): This means that \( g(0) = 4 \).
2. **Function \( f(x) \)**:
- Crosses the x-axis at \((2, 0)\): This means that \( f(2) = 0 \).
- Crosses the y-axis at \((0, 4)\): This means that \( f(0) = 4 \).
From this information, we can draw a few conclusions about the functions:
- Both \( g(x) \) and \( f(x) \) have the same y-intercept at \( (0, 4) \).
- \( g(x) \) has an x-intercept at \( x = -2 \), while \( f(x) \) has an x-intercept at \( x = 2 \).
- Since both functions are upward arcs, it can be inferred that they are both parabolic functions, but they open in different directions horizontally with respect to the x-axis.
In summary, the true statement regarding the graphed functions is that they share the same y-intercept but cross the x-axis at different points: \( g(x) \) at \( x = -2 \) and \( f(x) \) at \( x = 2 \).