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1. Find the vertex of the parabola f(x) = x² - 8x + 16.
   Solution: x=-b/2a=-(-8)/2*1=4, y=4² - 8*4 + 16=0, i.e coordinates of the vertex are (4, 0) 
   
   
2. Find the x- and y-intercepts of the cubic function f(x) = (x-3)(2x-10)(x+4).
   Solution: (x-3)(2x-6)(x+4)=0 which gives: (x-3)=0, (2x-10)=0, (x+4)=0. Solving each of these equations for x gives: x=3, x=5, and x=-4
   
   
3. If  f(x) = x²-4x+6  and  g(x) = 2x²-5x+10, find (f-g)(x).
   Solution: x²-4x+6 - (2x²-5x+10) = x²-4x+6 - 2x²+5x-10=- x²+x-4 
   
   
4. If  f(x) = x+4  and  g(x) = 2x²-x-1, evaluate the composition (g o f)(2).
   Solution: substitute f(x) for x in g(x): (g o f)(x)= 2(x+4)²-(x+4)-1= 2x²+16x+32 -x-5=2x²+15x+27
   Now, substitute 2 for x: (g o f)(2)= 2(2)²+15(2)+27=8+30+27=65
   An alternative way to solve this problem: calculate f(2)=2+4=6 and substitute it in g(x)=2(6)²-6-1=65
   
   
5. If  f(x) = x+4  and  g(x) = 2x²-x-1, find the composition (f o g)(x).
   Solution: (f o g)(x)= (2x²-x-1)+4=2x²-x + 3
   
   
6. Write the following sentence as an equation:  y varies directly as x.
   Solution: y=kx
   
   
7. Write the following sentence as an equation:  x is directly proportional to y and is inversely proportional to the cube of z.
   Solution: x=ky/z³
   
   
8. What are the zeros of the parabola:  f(x) = x² - 7x + 10 (that is, what are the x-intercepts or the points where the graph crosses the x-axis)?
   Solution: x² - 7x + 10=0. This expression can be factored as: (x-2)(x-5)=0 i.e.  (x-2)=0, (x-5)=0, i.e x=2, x=5
   
   
9. What is the vertical asymptote of the rational function f(x) = 3x / (2x - 1)?
   Solution: 2x-1=0, x=1/2 - vertical asymptote
   
   
10. What is the horizontal asymptote of the rational function f(x) = 3x / (2x - 1)
    Solution: When x is approaching infinity, we can simplify denominator as 3x/2x=3/2 - horizontal asymptote

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