Question
Consider the functions shown on the graph.
A coordinate grid with two lines. One line labeled f(x) and passes through (negative 3, 1), (0, 1), and point (1.5, 1). The second line is labeled g(x) and passes through point (0, negative 1), point (1.5, 1), and point (3, 3).
What is the best approximation for the input value when f(x)=g(x)?
0.0
0.5
1.5
3.0
A coordinate grid with two lines. One line labeled f(x) and passes through (negative 3, 1), (0, 1), and point (1.5, 1). The second line is labeled g(x) and passes through point (0, negative 1), point (1.5, 1), and point (3, 3).
What is the best approximation for the input value when f(x)=g(x)?
0.0
0.5
1.5
3.0
Answers
GPT-4o mini
To find the best approximation for the input value when \( f(x) = g(x) \), we need to identify the points where the two functions intersect.
From your description:
- The function \( f(x) \) is a horizontal line that has a constant value of 1, passing through the points \((-3, 1)\), \((0, 1)\), and \((1.5, 1)\).
- The function \( g(x) \) has points \((0, -1)\), \((1.5, 1)\), and \((3, 3)\). It appears to be a sloped line.
The function \( f(x) = 1 \) intersects the graph of \( g(x) \) at the point \((1.5, 1)\), since at \( x = 1.5 \), both functions have the same output value of 1.
To summarize:
- \( f(1.5) = 1 \)
- \( g(1.5) = 1 \)
Thus, the best approximation for the input value when \( f(x) = g(x) \) is \( 1.5 \).
From your description:
- The function \( f(x) \) is a horizontal line that has a constant value of 1, passing through the points \((-3, 1)\), \((0, 1)\), and \((1.5, 1)\).
- The function \( g(x) \) has points \((0, -1)\), \((1.5, 1)\), and \((3, 3)\). It appears to be a sloped line.
The function \( f(x) = 1 \) intersects the graph of \( g(x) \) at the point \((1.5, 1)\), since at \( x = 1.5 \), both functions have the same output value of 1.
To summarize:
- \( f(1.5) = 1 \)
- \( g(1.5) = 1 \)
Thus, the best approximation for the input value when \( f(x) = g(x) \) is \( 1.5 \).