Please complete the table and answer all 4 questions according to the proper function. Please do not use any form of e or ln, differentiation, integration, or derivatives in any of the answers. Please do not use AI to solve as it often wrong and easily evident.

1. A sum or difference of two functions with at least one max or min. Function: f(x)=log x - sin x	1. State the Local Max and Local Min. Justify answer with reference to the graph of this function and the sign of IRC. Provide a sketch on paper of the function
2. A product of two functions with at least one x intercept. Function: f(x)=1/8 x3 sin x	2. Determine the x intercepts and y intercept. Justify answer with calculations and show algebraic steps to determine the x intercepts and the y intercept.
3. A quotient of two functions. Function: f(x)=log x/sin x	3. State the Domain, Range and vertical or horizontal Asymptotes. Justify answer with reference to equation and graph. Provide a sketch on paper of the function.
4. A composite function. Function: f(x)= sin (2x+3/x-1)	4. Determine the Instantaneous Rate of Change at x=A. Choose a value for A in the domain of the function and show full calculations. Is the function increasing at that point? How do you know?