Final answer:
Abigail's claim that y=5x^3-2 is not a linear function is supported by the fact that the graph of this function will not form a straight line, which is characteristic of linear functions.
Step-by-step explanation:
Abigail is correct; the function y=5x^3-2 is indeed a function, but it is not a linear function. Linear functions are of the form y = a + bx, where 'a' is the y-intercept and 'b' is the slope of the line. In linear functions, 'b' remains constant, indicating that the slope is the same at all points along the line. The graph of a linear function is always a straight line.
The reason Abigail's claim is true is justified by option d) the graph of the function does not form a straight line. The coefficient of x^3 indicates that the function is a cubic function, which means its graph will be a curve, not a straight line. Though the graph can increase or decrease and may or may not contain specific points like (0,0), these characteristics do not define linearity. Linearity is solely determined by the graph forming a straight line, which this function does not do due to the x^3 term.