Final answer:
The function that could pass through the points (-4, 48) and (-1, 6) can be found by calculating the slope, which is -14. The only given equation that matches this slope is C. y = -14x - 8; no other options provided that are linear match this slope.
Step-by-step explanation:
The student is asking which functions could pass through the points (-4, 48) and (-1, 6). To determine the possible functions, we need to calculate the slope of the line passing through these points and find a function with a matching slope that will pass through one of these points.
To find the slope (m), use the formula m = (y2 - y1) / (x2 - x1). Plugging in the values:
m = (6 - 48) / (-1 - (-4))
m = (-42) / (3)
m = -14
Now, we have the slope and can use the point-slope form of a line equation, which is y - y1 = m(x - x1). We can use one of the points to find the equation:
y - 6 = -14(x - (-1))
y - 6 = -14(x + 1)
y = -14x - 14 + 6
y = -14x - 8
Therefore, the equation C. y = -14x - 8 could represent this function.
Since the problem states to select two possible equations, we will need to find one more equation that satisfies these points. Let's check option A: y = -3(2)^x. This is an exponential function, and without further information, we cannot definitively say it passes through the given points. Option B, y = 14(2)^x, is also an exponential function, so the same applies. Option D: y = 3(2)^x doesn't match the slope we found, so it cannot represent the function passing through the two points.
Given the options and the fact that the slope must be -14, we can conclude that only option C is correct. The second correct equation is not listed among the options, which implies that there might be a typo or that we only have one correct answer provided.