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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)

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You are given the following. The translation of g of x is equal to y is 1 plus the quantity 1.5 raised to the power of x is equal to g(x) = y = 1 + (1.5ˣ). The translation of the straight line f of x joins ordered pairs (4, 1) and (2, -3). The straight line p(x) joins the ordered pairs (0, 2) and (1, -5).

To get the equation of f(x), apply point - slope formula.
(4, 1) and (2, -3)
y - y1 = m(x - x1)
y - 1 = (-3 -3/ 2 - 4)(x - 4)
y - 1 = 3(x - 4)
y - 1 = 3x - 12
y = 3x - 11

To get the equation of p(x), apply point - slope formula.
(0, 2) and (1, -5)
y - y1 = m(x - x1)
y - 2 = (-5 - 2/ 1 - 2)(x - 0)
y - 2= 7(x)
y = 7x + 2

To answer part A, equate the functions of f(x) and p(x)
3x - 11 = 7x + 2
4x = -13
x = -13/4

substitute this answer to any of the two functions to get y
y = 3x - 11
y = 3(-13/4) - 11
y = -83/4

The solution is then (-13/4, -83/4).