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 p(x) and f(x)? (3 points)

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

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

Answer 1

Part A: the solution to the pair of equations represented by p(x) and f(x) is (-3, -3)

Part B: (0, 0), (3, 3)

Part C: the solution to the equation p(x) = g(x) is (-6, 1)

Answer 2

Part A)
`(-3,-3)`

Part B)
`(0,0)` and point
`(5,5)`

Part C)
`x=-6`

Explanation:

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

we know that

The solution to the pair of equations represented by p(x) and f(x) is the intersection point both graphs

In this problem the intersection point is equal to
`(-3,-3)`

Part B) Write any two solutions for f(x)

we know that

If a ordered pair is a solution of the function f(x)

then

the ordered pair belong to the graph of the function f(x)

so

the point
`(0,0)` and point
`(5,5)` belong to the graph of f(x)

therefore

the point
`(0,0)` and point
`(5,5)` are solutions of the function f(x)

Part C) What is the solution to the equation p(x) = g(x)?

we know that

The solution of the equation

`p(x) = g(x)`

Is the x-coordinate of the intersection point both graphs

so

`x=-6`