please help with pre cal. please help with each part of the question.

4. Sketch the graph of f(x)= x? 2x 8 using the Vertex and the X-intercept. Identify the axis of symmetry. 5. Sketch the graph of the function f(x)= ? using the intersections with the axes and the asymptotes (if any). State its domain. 6. Find all the \"zeros\" of the function f(x)=x3 4 x% + 9x 36 if you know x=4 is a root of f. 7. Given f(x)=x-1 and g(x)=5 2x?, find g(f(x)). 8. Sonia invests 7800$ at an annual interest rate of 3%, compounded continuously. How long will it take her money to double? Use A=Pe. 9. Evaluate: a) log,5 b) log(log1000000) ) logs9logy225 d) 7log73 10. Define the new functions based on the transformations of the initial functions: a) g(x)is obtained by shifting f(x)= 3* four units to the left; b) h(x) is obtained by shifting f(x)=log,;x one unit downward. 15. Use the values sec x =4 and sin > 0 to find the values of all six trigonometric functions. 16. Solve: a) 32%= 27 b) 2%71=9 17. Solve: a) log (x2 + 4)=1 b) log,5-log;x=10 18. Find the exact value for: a) tan ? b) sec 1110 19. Factor: cos'X-Cosx-6 20. Verify the identity: cscx -sinx = cosxcotx 21. Verify the identity: tan20 1-cose 1+seco cose11. From a point on the ground 180 feet from the base of a water tower, the angle of elevation of the top of tower is 83.6. Find the height of the tower. 12. For a wedding on a river, a drone which is 9200 feet above the surface it measures the angle of depression of a boat to be 52. How far is the boat from the point on the surface directly below the drone? 13. Sketch the graph of g(x)= % sin7x, using the amplitude and the period. 14. Sketch the graph of g(x)= 3 sin4x, using the amplitude and the period. 1. The point (-1,2) lies on the circle whose center is at (4,-7). Write the standard form of the equation of this circle. 2. Find the domain for the following functions: ) x ) 2 ) 8x1 ) x%-x % Vx-5 x2+x42 x2+423 x9 3. For the function f(x)= 5x 2 apply the difference quotient m and simplify your