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)

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.

i believe the answer is the polygon, heptagon.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is