Final answer:
The graph of f(x)=10x–10 is transformed into g(x)=-10x+10 through a reflection over the y-axis and a vertical shift upwards by 20 units.
Step-by-step explanation:
The transformation that converts the graph of f(x)=10x–10 into the graph of g(x)=-10x+10 is a combination of two transformations: a reflection over the y-axis followed by a vertical shift. The reflection is evident because the coefficients of x are opposites in sign, meaning the slope of the graph has changed from positive to negative. This reflects the graph across the y-axis. The vertical shift is seen in the constant term of the equation changing from -10 to +10. This shifts the graph upwards by 20 units.
To visualize this transformation, consider labeling the graph with f(x) and x, and scaling the x and y axes appropriately. For the original function f(x), where f(x) = 10 at x = 1 and the domain is 0≤x≤ 20, one can easily sketch a straight line with a slope of 10 and y-intercept of -10. After the transformations, the line for g(x) will have a slope of -10 and a y-intercept of 10.