Final answer:
The question involves understanding function transformations, specifically reflections. Diagram 2 shows a modified graph of function g(x), and interpreting this involves knowledge of graph reflections across the axes and the impact on the graph's shape, similar to understanding the slope and y-intercept in straight-line equations.
Step-by-step explanation:
The student's question pertains to transforming functions and understanding how the graph of a function changes when its equation is modified. When the value of y changes as a function of x, a graph can illustrate these changes using specific values for (x,y) data pairs. If Diagram 1 shows a function y = g(x), and Diagram 2 depicts a transformation of this function, the correct transformation must reflect the particular modification applied to the function in terms of reflection, scaling, or shifting.
An example of a transformation is y = -g(x), which reflects the function g(x) over the x-axis, changing the sign of all y-values. When we see y = g(-x), this represents a reflection of g(x) over the y-axis, flipping the function horizontally. Understanding these principles can be applied to interpreting straight-line graphs, characterized by a slope and y-intercept, as illustrated in Figure A1, where the slope of the line is noted as a rise of 3 for every run of 1 on the horizontal axis, and the y-intercept is 9.