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)
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.