Two input-output pairs for function f(x) are (−6,52) and (−1,172) . Two input-output pairs for function g(x) are (2,133) and (6,−1) . Paige says that function f(x) has a steeper slope. Formulate each function to assess and explain whether Paige's statement is correct.(4 points)

Question

Two input-output pairs for function  f(x)  are  (−6,52)  and   (−1,172) . Two input-output pairs for function  g(x)  are  (2,133)  and   (6,−1)  . Paige says that function  f(x)  has a steeper slope. Formulate each function to assess and explain whether Paige's statement is correct.(4 points)

GPT 3.5 · Answer

To assess Paige's statement, we need to find the slopes of the functions f(x) and g(x) using the input-output pairs.

For function f(x):
The slope is calculated as:
slope_f = (change in y)/(change in x) = (y2 - y1)/(x2 - x1)
Taking the points (−6,52) and (−1,172):
slope_f = (172 - 52)/(-1 - (-6)) = 120/5 = 24

For function g(x):
The slope is calculated as:
slope_g = (change in y)/(change in x) = (y2 - y1)/(x2 - x1)
Taking the points (2,133) and (6,−1):
slope_g = (-1 - 133)/(6 - 2) = -134/4 = -33.5

Since the slope of f(x) is 24 and the slope of g(x) is -33.5, we can see that the slope of f(x) is steeper than the slope of g(x). Therefore, Paige's statement is correct.