Question

Can you please answer this?

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

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

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

Answer 1

A. (1, -1)

B. (1, -1), (2, 0)

C. x = 0

Explanation:

A graph is a plot of all the points that are solutions to an equation.

Part A:

A point will be a solution to two equations if it is a point of intersection of their graphs. The one point that is a solution to both p(x) and g(x) is the one point where their graphs intersect: the red and blue lines cross at (1, -1).

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Part B:

Any other point on the graph p(x) will be another solution of it. One that is near to the point of intersection with g(x) is the point where p(x) crosses the x-axis: (2, 0). Of course, the solution listed in Part A is also a solution to p(x).

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Part C:

The point where the graph of g(x) crosses the graph of f(x) is (0, 3). The x-value that makes g(x) = f(x) is x=0. That is the solution to this equation. (We don't really care what the values of f(0) and g(0) are--just that they are equal.)