Please answer the question step by step.

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1. The point (1-3) lies on the circle whose center is at (-2,5). Write the standard form of the equation of this circle. 1. Find the domain for the following functions: a) 3x b) 2 C) 147 x -+2x Y*+x-12 d' x+4 3. Find the quotient and the remainder for (x* + 8x] - 6x - 3 ) = (x + 2). 4. For the function f(x)=2x - 3 apply the difference quotient - and simplify your answer. 5. Sketch the graph of f(x)= x2 - 4x + 4 using the Vertex and the X-intercept. Identify the axis of symmetry. 6. Find all the "zeros" of the function f(x)=x3 - 5 x2 + 4x - 20 if you know x=5 is a root of f. 7. Given the function f(x)= x'. a) Find the function g(x) performing on f(x) a reflection in the X-axis followed by a downward shift of 4 units; b) Find the function h(x) performing on f(x) an horizontal shift of five units to the left followed by a reflection in the X-axis. 5. Given f(x)=x+1 and g(x)=2 - x3, find g(f(x)). 9. Given f(x)= x2+5 and g(x)=3x2 - 5x + 7, find (f-g)(x). 10. Sketch the graph of the function f(x)= 1x-3 using the intersections with the axes and the asymptotes (if any). State its domain