The graph shows the functions f(x), p(x), and g(x): graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to the power of x. the straight line f of x joins ordered pairs 4, 1 and 2, negative 3 and is extended on both sides. the straight line p of x joins the ordered pairs 0, 2 and 1, negative 5 and is extended on both sides. courtesy of texas instruments 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)

Part A:

Given that the straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by



Thus, p(x) = -7x + 2

Given that the straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by



Thus, f(x) = 2x - 7

The solution to the pair of equations represented by p(x) and f(x) is given by

p(x) = f(x)
⇒ -7x + 2 = 2x - 7
⇒ -7x - 2x = -7 - 2
⇒ -9x = -9
⇒ x = -9 / -9 = 1

Substituting for x into p(x), we have

p(1) = -7(1) + 2 = -7 + 2 = -5

Therefore, the solution to the pair of equations represented by p(x) and f(x) is  (1, -5)

Part B:

From part A, we have that f(x) = 2x - 7

when x = -8

f(-8) = 2(-8) - 7 = -23

Thus, (-8, -23) is a solution to f(x).

When x = -10

f(-10) = 2(-10) - 7 = -27

Thus, (-10, -27) is a solution to f(x).

Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).

Part C:

From part A, we have that p(x) = -7x + 2, given that

From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).

Therefore, the solution to the equation p(x) = g(x) is (0, 2).