Transformations
Which transformation causes a graph to move up, left, right, or down?
Translation
What does the graph of an absolute value function look like?
V shaped
What does the graph of a quadratic function look like?
U shaped
What does the graph of a cubic function look like?
Squiggle shape
What does the graph of a square root function look like?
Curved line
Which transformation causes a function to flip over the x-axis and y-axis?
Reflection
Given the parent function f(x) = |x|
Which function represents a translation left 5 units and down 5 units?
A. y= f(x+5)−5
B. y= f(x−5)−5
C. y=f(x+5)+5
D. y=f(x−5)+5
A
Given the parent function f(x) = x2
Which function represents a reflection over the y-axis and translation one units to the left.
A. y=f(-x+1)
B. y=−f(x−1)
C. y=f(−x)−1
D. y=f(−x)+1
A. y=f(-x+1)
f(x) + d
What type of transformation does + d outside of the parenthesis represent?
Vertical translation up d units
Given the parent function f(x) = sqrt x
What new function shows a translation two units up and two units to the right.
A. y = f(x+2)+2
B. y = f(x−2)−2
C. y = f(x+2)−2
D. y = f(x−2)+2
D. y = f(x−2)+2
f(x) = x2
Show us a new function that represents a translation left 3 units and down 2 units.
f(x) = (x+3)2-2
Given the parent function f(x) = |x|
Which function represents a reflection over the y-axis and translation 1 unit up?
A. y=−|x−1|
B. y= |-x|+1
C. y= -|x+1|
D. y= |-x|-1
B. y= |-x|+1
Given the parent function f(x) = x2
Which function represents a translation two units to the right and one unit down.
A. y=f(x+2)+1
B. y=f(x+2)−1
C. y=f(x−2)+1
D. y=f(x−2)−1
D. y=f(x−2)−1
f(-x)
what transformation does the negative symbol inside the parenthesis represent?
Reflection over the y-axis
Given the parent function f(x) = sqrt x
What new function shows a reflection over the x axis and a translation 4 units to the left
A. y = −f(x+4)
B. y = f(−x)−4
C. y = f(−x)+4
D. y = −f(x−4)
A. y = −f(x+4)
Given f(x) =x2
Show us a new function that represents a reflection over the x-axis and horizontal stretch.
f(x) = -(1/2x2)
Given the parent function y = |x| create a new function that represents a translation right 4 units and reflection over the x axis.
y = -|x-4|
Given the parent function f(x) = x2, write a new function that represents a reflection over the x axis, translation up 2 units and to the right 7 units.
f(x) = -(x-7)2 +2
f(x+c)
What transformation does adding c inside the parenthesis represent?
Horizontal translation left c units
Given the parent function f(x) = √x, write a new function that represents a reflection over the x-axis and right 3 units.
y=−f(x−3)
Given f(x) = |x|
Show us a new function that represents a reflection over the y-axis, translation down 2 units, translation to the right 3 units, and a vertical stretch by 2.
f(x) =|-2x-3|-2
Given the parent function y = |x| create a new function that represents a translation up 6 units, reflection over the y axis, and translation left 5 units.
y = |-x+5|+6
Given the parent function f(x) = x2, write a new function that represents a horizontal shrink by 3, reflection over the y axis, and translation to the left 3 units.
f(x) = (-3x + 3)2
f(bx)
if b, the number in front of x, is a fraction what type of transformation does it represent?
A horizontal stretch
Given the parent function f(x) = √x, write a new function that represents a reflection over the y-axis and down 1 unit.
y=f(−x)−1