Transformations
right 3, down 5
Identify the domain, range, and number of real roots of the following graph.
domain: (-infinity, infinity)
range: [-6, infinity)
# of real roots: 4
Factor completely: x3 + 27
(x + 3)(x2 + 3x + 9)
Divide (3x2 + 7x - 12) / (x+2)
3x + 1 + (-14/(x+2))
Write an equation of a cubic function that is reflected across the x-axis and translated 3 units right and 6 units down.
Fill in the two end behavior statements and identify if the leading coefficient is positive or negative.
x --> infinity, f(x) --> infinity
x --> -infinity, f(x) --> infinity
leading coefficient: positive
Factor completely: x3 - 27
(x - 3)(x2 + 3x + 9)
Divide (2x3 - 3x2 + 7x - 6) / (x-2)
2x2 + x + 9 + 12/(x-2)
Identify transformations of f(x) = 1/2 (x+3)^3 - 2
vertical compression by a factor of 1/2, left 3, down 2
Identify increasing and decreasing intervals.
inc: (-5, -1), (5, infinity)
dec: (-infinity, -5), (-1, 5)
Factor and find the zeros of x3 - 3x2 - 4x + 12
(x-3)(x+2)(x-2)
x = 2, -2, 3
Divide (3x3 + 7x2 - 12x - 8) / (x2-3)
3x + 7 + (-3x+13)/(x2 - 3)
Write an equation of a cubic function that is reflected across the x-axis, horizontally compressed by a factor of 3, and translated 2 units left and 4 units up.
-(3(x+2))^3 + 4
Identify local max and local min.
local max: (-1, 3)
local mins: (-5, -6), (5, -3)
Factor and find the zeros of x3 - 5x2 - 9x + 45
(x-5)(x+3)(x-3)
x = 5, -3, 3
Divide (2x3 - 5x2 + 12x - 21) / (x2+4)
2x - 5 + (4x-1)/(x2 + 4)
Identify transformations of f(x) = 2(-(x+4))^3 - 5
vertical stretch by a factor of 2, horizontal reflection, left 4, down 5
Identify domain, range, # of real roots, if the leading coefficient is positive or negative, increasing and decreasing intervals, local max, and local min.
domain: (-infinity, infinity)
range: (-infinity, infinity)
# of real roots: 5
x --> infinity, f(x) --> infinity
x --> -infinity, f(x) --> -infinity
leading coefficient: positive
inc: (infinity, -6), (-4, 1), (3, infinity)
dec: (-6, -4), (1, 3)
local max: (-6, 4), (1, 2)
local min: (-4, -8), (3, -7)
Factor and find the zeros of x3 + 4x2 - 25x + 100
(x+4)(x-5)(x+5)
x = 4, 5, -5
Divide (2x4 - 3x3 - 17x2 - 8x - 5) / (x-4)
2x3 + 5x2 + 3x + 4 + 11/(x-4)