Question

1. the functions f(x) and g(x) are graphed to the side. approximate the value x when f(x) = g(x). a) x = 2.5 b) x = -0.9 c) x = 3.5 d) x = -1

Explanation:

Step1: Recall the meaning of \( f(x) = g(x) \)

When \( f(x) = g(x) \), the graphs of \( f(x) \) and \( g(x) \) intersect. So we need to find the \( x \)-coordinate of the intersection point of the two graphed functions.

Step2: Analyze the graph

Looking at the graph (even with partial view), the intersection point's \( x \)-value should be approximated. Let's check the options:

• Option a: \( x = 2.5 \) – Let's see the grid. If we assume the grid has integer - spaced lines, the intersection seems around \( x = 2.5 \) (since it's between \( x = 2 \) and \( x = 3 \), closer to the middle or a bit more, 2.5 is a reasonable approximation).
• Option b: \( x=- 0.9 \) – The intersection is not on the negative side (from the partial graph, the intersection is on the positive \( x \)-side).
• Option c: \( x = 3.5 \) – 3.5 is to the right of where the intersection seems (the intersection is before \( x = 3.5 \) if we consider the lines' slopes).
• Option d: \( x=-1 \) – Again, the intersection is on the positive \( x \)-axis, not negative.

Answer:

a) \( x = 2.5 \)