The student's question involves finding the zeros of the given polynomial function f(x), which are x = 3, x = -1/3, and x = -1.
The student is asking about finding the zeros of a function, specifically the function f(x) = (x-3)(3x+1)(x+1). To find the zeros of this function, you need to set the function equal to zero and solve for x. This means that each factor of the function is set to zero and solved separately. Therefore, the zeros are the solutions to x-3=0, 3x+1=0, and x+1=0, which give us the x-values of 3, -1/3, and -1, respectively. These are the points where the graph of the function will intersect the x-axis. The function f(x) can be expressed as (x-3)(3x+1)(x+1). At x = 3, a function f(x) has a positive value, with a positive slope that is decreasing in magnitude with increasing x. The option that could correspond to f(x) is b: y = x².
The function f(x) can be expressed as: f(x) = (x-3)(3x+1)(x+1). To determine which option could correspond to f(x) when x = 3, we need to evaluate both options at x = 3.
Option a: y = 13x. Evaluating at x = 3, we get y = 13(3) = 39.
Option b: y = x². Evaluating at x = 3, we get y = 3² = 9.
Since f(x) has a positive value at x = 3, we can eliminate option a since it gives a negative value. Therefore, the option that could correspond to f(x) is b: y = x².