Is it a polynomial?
5x+1
Yes!
When the graph crosses the x-axis.
x-intercept
What transformations occurred?
y=x3+2
up 2
Simplify.
(x+2)+(3x-7)
4x-5
Factor.
4x3-12x2-5x+15
(4x2-5)(x-3)
x1/2-6
No, because there is a fraction exponent.
The set of all y-values in a function
range
What transformations occurred?
y=(x-4)3
right 4
Simplify.
(3x2-4x)-(x2-5x)
2x2+x
Factor.
7x3-28x2+5x-20
(7x2+5)(x-4)
3x3-7x-4+2
No, because there is a negative exponent.
A high point on the graph, but there are points that are higher
local maximum
What transformations occurred?
y=-x3-7
reflect over the x-axis, down 7
Simplify.
4x(-3x3-5x2+2x)
-12x4-20x3+8x2
Factor.
8x3-64x2+x-8
(8x2+1)(x-8)
7x8-x2+9x4-2
Yes!
When the ends of the graph go in the same direction
even function
What transformations occurred?
y=.5(x+2)3
vertically compress and left 2
Simplify.
(3x-7)(2x4-6x2+1)
Factor.
12x3-21x2+28x-5
(3x2+7)(4x-7)
(2x2-7)/(3x+4)
No, because there is a variable in the denominator.
These two things will NOT be present if the function is ODD
absolute maximum and absolute minimum
What transformations occurred?
y=-4(x-5)3-9
reflect over the x-axis, vertically stretch, right 5, down 9
Simplify.
(x3-5x2-2x+24)/(x-3)
x2-2x-8
Factor.
6x3-16x2+21x-56
(2x2+7)(3x-8)