Transformations
What is the transformation that happens?
f(x)=x2 to the function f(x)=x2+3
Moves up 3 units
Factor x2-7x-8
(x-8)(x+1)
How do you find the inverse of a function algebraically?
Switch the x and y variables and then solve for y.
Out of the following: Which factor do you cross out, and which do you set equal to zero?
Vertical asymptotes are set equal to zero, and holes are cancelled out.
If the highest power on x in the numerator is GREATER than the highest degree in the denominator, then the horizontal asymptote is...
None
What is the transformation that happens?
f(x)=x2 to f(x)=(x+2)2
It moves left two units
Factor 4x2 + 12x + 5
(2x + 5)(2x + 1)
Find the inverse of y=(x-3)3
y=x1/3+3
(cubed root of x)
What is the hole for the equation (x2+6x+8)/(x2-x-6)?
Hole at x=-2
If the highest power on x in the numerator is LESS than the highest degree in the denominator, then the horizontal asymptote is...
y=0
Write the function of the regular y=x2 function when you have a vertical stretch of 3, right 1, and down 2.
y=3(x-1)2-2
Factor 6x2 - 19x - 7
(2x - 7)(3x + 1)
Find the inverse of y=(3)/(x-1)
y=(3/x)+1
What is the vertical asymptote of (x2+7x-8)/(x2-5x+4)
V.A. at x=4
Find the horizontal asymptote of (x3+1)/(x2)
None
Write the function of the regular y=x2 function when you have a vertical compression of 1/4, left 3, a reflection, and up 1.
y=-(1/4)(x+3)2+1
factor 10x2 + x - 2
(5x - 2)(2x + 1)
Find the inverse of y=(5x-15)/2
y=(2x+15)/5
Find BOTH the vertical asymptote and the hole for
(x2-9)/(x2-3x-18)
V.A. at x=6
Hole at x=-3
Find the horizontal asymptote of (x2+3x-7)/(5x2)
y=1/5
If you create transformations on a graph y=x2, does the domain and range of the new function change? If yes, why?
The domain never changes, it will always be all real numbers. The range changes based on where the vertex of the parabola is on the graph.
Factor 6x2 - 16x + 10 *HINT* factor out the greatest common factor first!
2(x - 1)(3x - 5)
Are the two functions inverses of each other? *HINT* use composition of functions! f(g(x)) and g(f(x))
f(x)=10x+5 g(x)=(x-5)/10
Find the V.A. and the hole of (x2-7x+12)/(x2+8x+12)
V.A. at x=-6 and x=-2
NO HOLE
Find the horizontal asymptote of 3/(x-5)
y=0