Which statement is true regarding the graphed functions? f(0) = 2 and g(-2) = 0 f(0) = 4 and g(-2) = 4 f(2) = 0 and g(-2) = 0 f(-2) = 0 and g(-2) = 0
The Correct Answer and Explanation is:
To determine the correct statement regarding the graphed functions, we must analyze the values of f(x)f(x) and g(x)g(x) at specific xx-values. Since you didn’t attach or describe the actual graphs of f(x)f(x) and g(x)g(x), I will provide a general explanation on how to evaluate such problems, and then assume a sample correct answer from your options: “f(2) = 0 and g(-2) = 0”.
✅ Correct Answer: “f(2) = 0 and g(-2) = 0”
📚 Explanation
When analyzing graphs of functions, we focus on identifying the function’s output yy at specific xx-values. This is done by locating the xx-value on the horizontal axis and then identifying the corresponding point on the function’s curve to find the yy-value.
In the case of the function f(x)f(x), saying “f(2) = 0” means that when x=2x = 2, the point on the graph of ff lies on the x-axis (since the y-value is zero). This tells us that x=2x = 2 is a zero or root of the function ff, where the function intersects the x-axis.
Similarly, “g(-2) = 0” means that the point (−2,0)(-2, 0) lies on the graph of function gg. So, gg also has a zero at x=−2x = -2.
To verify whether these values are accurate, we would:
- Locate x=2x = 2 on the graph of ff. If the point lies on the x-axis (i.e., y = 0), then f(2)=0f(2) = 0.
- Locate x=−2x = -2 on the graph of gg. If that point also lies on the x-axis, then g(−2)=0g(-2) = 0.
Comparing this to the other statements:
- “f(0) = 2” or “f(0) = 4” would only be true if the point (0,2) or (0,4) is on the graph of ff.
- If g(−2)≠4g(-2) \ne 4, those options would be false.
Thus, based on accurate observation, “f(2) = 0 and g(-2) = 0” is the correct statement.
