To determine where \( f(x) = g(x) \), we need to find the points of intersection between the two functions \( f \) and \( g \).
Given the characteristics of the graphs:
- \( f(x) \) is a horizontal line that crosses the y-axis at \( y = 4 \). Hence, \( f(x) = 4 \) for all values of \( x \).
- \( g(x) \) is a curve that crosses the x-axis at \( (-2, 0) \) and the y-axis at \( (0, 4) \). The y-intercept at \( (0, 4) \) means that \( g(0) = 4 \).
Since \( f(x) \) is always 4, we need to find where \( g(x) = 4 \).
From the graph:
- We know from the \( y \)-intercept that \( g(0) = 4 \).
- Therefore, \( f(0) = g(0) \).
Given the options:
- The valid statement is based on these details where \( f(x) = g(x) \) at \( x = 0 \), which matches \( f(0) = g(0) \).
The correct answer is:
\[ f(0) = g(0) \]
Thus, the correct choice is:
\[ f(–4) = g(–4) \text{ and } f(0) = g(0) \]
Two functions are graphed on the coordinate plane.
On a coordinate plane, a 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 straight horizontal line, labeled f of x, crosses the y-axis at (0, 4).
Which represents where f(x) = g(x)?
f(4) = g(4) and f(0) = g(0)
f(–4) = g(–4) and f(0) = g(0)
f(–4) = g(–2) and f(4) = g(4)
f(0) = g(–4) and f(4) = g(–2)
1 answer
1 answer