Polynomial Rules
Is y = 6x4+3x3+2x2-x-1
a polynomial?
No
Does the A value effect the x or y values?
If |A| <1, then does the graph compress or stretch?
y
compress
List the correct order of the transformations for y=-x2
Vertical: vertically reflected
Horizontal: None
List the x-intercepts as coordinates for f(x) = (x-2)(x+1)
(2, 0) , (-1,0)
What is the end behavior of y=-2x?
up, down
In y = (x-3)4, does the graph pass through or bounce off the x-axis?
bounce off
Does the D value change the x or y values?
Which way does the graph move is the D value is negative?
y
down
List the correct order of the transformations for y=-2|x-2|
Vertical: vertically reflected, vertical stretch by 2,
Horizontal: right 2
List the x-intercepts as coordinates for x2+10x+16
(x+8)(x+2)
x-intercepts: (-8,0) (-2,0)
What are x-intercepts of y=x2-8x+12?
What is the end behavior?
y = (x - 6)(x -2)
x-intercepts: (6,0) (2, 0)
end behavior: up, up
In y = (x-3)3, does the graph (pass through straight on/bounce off/pass through curved on) the x-axis
pass through curved on
Does the C value change the x or y values?
f(x) is transformed to f(x-2), then which way did the graph move?
x
right 2
List the correct order of the transformations for y=2|x|+4
Vertical: vertical stretch 2, up 4
Horizontal: None
List the x-intercepts as coordinates for y=x3-625x
y=x(x2-625)
y=x(x+25)(x-25)
x-intercepts: (0,0), (-25,0), (25,0)
For f(x) = (x+1)(x-3)2 ,what is the end behavior?
At what x-intercept does the graph bounce off the x-axis?
down, up
bounce (3, 0)
What is the end behavior for this function:
y= -3x(x+1)2(x-2)5(x-3)2
down, down
Does the B value change the x or y values?
If B = 2, how does it tranform the parent function?
x
horizontally compress 0.5
List the correct order of the transformations for y=|2x-4|
If not factored: right 4, then horizontal compression of 1/2
If factored like this y=|2(x -2)|, then
horizontal compression 1/2, followed by right 2
List the x-intercepts as coordinates for y=x4-81x2
factor: x2(x2-81)
x2(x+9)(x-9)
x-intercepts: (0,0), (-9,0), (9,0)
For f(x) = -x3+16x, calculate end behavior and the x-intercepts.
State what happens at each x-intercept.
up,down
y=-x(x2-16)
y=-x(x+4)(x-4)
(0, 0) pass straight, (4, 0) pass straight, (-4,0) pass straight
Write in standard form AND list the end behavior.
y = 4x(x+1)(x-1)
y=4x3 - 4x
end behavior: down, up
What is the value of C in f(x) = 3|2x-6| + 4?
C = 3
List the correct order of the transformations for y=-4|6x-12|+2
factor: y=-4|6(x-2)|+2
Vertical: vertical reflection and vertical stretch by 4, then up 2
Horizontal: (If not factored) Right 12, then horizontal compression by 1/6 OR (If factored) Horizontal compression by 1/6, then right 2
List the x-intercepts as coordinates for y=x4-10x2+9
Hint (if needed): Let u = x2 , then factor the expression with u.
(x2-9)(x2-1)
(x+3)(x-3)(x+1)(x-1)
x-intercepts: (-3, 0), (3, 0), (-1, 0), (1,0)
For f(x) = x5-25x3 calculate end behavior and the x-intercepts.
State what happens at each x-intercept.
down, up
f(x) = x3(x2-25)
f(x) = x3(x+5)(x-5)
(0,0) pass curved, (5,0) pass straight, (-5,0) pass straight