Final answer:
The function A(x) = x is a linear equation of the form y = mx + b. Therefore, the corresponding function g(x) must also be a linear function, making option B the correct answer.
Step-by-step explanation:
The student asked about the function g(x). Based on the given function A(x) = x and the options provided, we must determine what type of function g(x) could be. The provided options are a constant value, a linear function, a quadratic function, and an exponential function.
The function A(x) = x is a linear equation because it has the form y = mx + b, where m (the slope) is 1, and b (the y-intercept) is 0. Therefore, the corresponding function g(x), which would have the same type of mathematical relationship, is a linear function as well. Examples of linear equations include y = -3x, y = 0.2 + 0.74x, y = -9.4 - 2x, etc., which all have the form y = mx + b with different values for m and b.
A quadratic function would be something like y = ax^2 + bx + c, which graphs to a parabola, and an exponential function follows the form y = a*b^x, which shows exponential growth or decay. Since A(x) is linear, option B, a linear function, is the correct answer for g(x).