Learn creatively: by modifying these problems & solving your own problems.
Just click Use this template button, change problems, solve, and click Publish button.
Please cross check other students' problems and comment.
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)
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
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
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
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
Write the following sentence as an equation: y varies directly as x. Solution: y=kx
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
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
What is the vertical asymptote of the rational function f(x) = 3x / (2x - 1)? Solution: 2x-1=0, x=1/2 - vertical asymptote
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