Question

PLEASE HELP!!! The graph shows the functions f(x), p(x), and g(x): Graph of function f of x is y is equal to 2 plus the quantity 1.5 raised to the power of x. The straight line g of x joins ordered pairs negative 1, 7 and 1, negative 1 and is extended on both sides. The straight line p of x joins the ordered pairs 2, 0 and 4, 2 and is extended on both sides. Courtesy of Texas Instruments 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)

Answer 1

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 - 12y = 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 + 24x = -13x = -13/4
substitute this answer to any of the two functions to get yy = 3x - 11y = 3(-13/4) - 11y = -83/4
The solution is then (-13/4, -83/4).
*~"AB84"~*