Question

The graph shows the functions f(x), p(x), and g(x):

Part A: What is the solution to the pair of equations represented by g(x) and p(x)? (3 points)

Part B: Write any two solutions for p(x). (3 points)

Part C: What is the solution to the equation g(x) = f(x)? Justify your answer. (4 points)

Answer 1

Answer:

• A. (x, y) = (1, -1)
• B. (1, -1), (2, 0)
• C. (0, 3). This is where their graphs cross, meaning g(x) = f(x) at that point.

Step-by-step explanation:

A solution to a pair of equations is the set of points where their graphs intersect. Points in that set will satisfy both equations, which is what "solution" means.

Here, the graphs of p(x) and f(x) each intersect the graph of g(x) in one place. Hence f(x) = g(x) has one solution, as does p(x) = g(x).

Finding the solution is a matter of reading the coordinates of the point of intersection from the graph.

A. The graphs interesect at x=1, y=-1.

B. Any point on the red line is a solution. We already know one of them from part A. Another is the x-intercept, where y=0. That point is (2, 0).

C. g(x) intersects f(x) at their mutual y-intercept: y = 3. x = 0 at that point.