Function Algebra
Factoring
Rational Functions
Quadratic Functions
100
Solve. Let f(x)= 4x+2, and g(x)=5x^2+2.
Find g(4) / f(4).
41/9
100
Factor out the GCF:
16x^3-10x^2+8x
2x(8x^2-5x+4)
100
Find the domain. Write interval notation for the answer.
f(x)= (x^2+1)/(x-4)
(-∞, 4) ∪ (4, ∞) All real numbers except 4.
100
Find the vertex of the parabola.
f(x)=2x^2 -12x+3
Vertex: (3, -15)
200
Let f(x)= 5x - 5 , and g(x)= 8x - 2
Find (f - g) (x).
-3x - 3
200
Factor by grouping:
10x^2-5x+6x-3
(2x-1)(5x+3)
200
Simplify.
(2x+16)/(2x-16)
(x+8)/(x-8)
200
Use the graph to find the vertex, the axis of symmetry, and the maximum or minimum value of the function.
Vertex: (2,-4)
Axis of Symmetry: x=2
Maximum value : -4
300
Let f(x)= x + 6 , and g(x)= x - 2
Find (f + g) (-3).
-2
300
Factor:
x^2-81
(x-9)(x+9)
300
Simplify.
(r^2-9)/(6r+18)
(r-3)/6
300
A projectile is thrown upward so that its distance above the ground after t seconds is h(t)= -16t^2+312t After how many seconds does it reach its maximum height?
10 secs
400
Let f(x)=(x-2)/4, and g(x)=4x+1
Find (g ∘ f) (26).
25
400
Factor:
x^2-3x-40
(x-8)(x+5)
400
Find the vertical asymptote(s) of the graph of the given function.
g(x)= (x+7)/(x-2)
x=2
400
Use factoring to find the exact solutions.
x^2-14x+40=0
{4, 10}
500
Let f(x)= 7x + 14, and g(x)= 4x - 1
Find (f ∘ g) (x).
28x + 7
500
Factor:
3x^2-11x-20
(3x+4)(x-5)
500
Find the horizontal asymptote, if any, of the rational function.
f(x)=(x+6)/(2x^2+7x-3)
y=0
500
Use the quadratic formula to find the exact solutions.
x^2+35=5x
5/2 +- (sqrt115)/2i