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Total questions: 50
Worksheet time: 2hrs 40mins
f(x) = 2x
Vertical stretch
Vertical compression
Vertical translation up
Reflection over the x-axis
No Transformation
f(x) = x2 - 6
Vertical translation up
Vertical translation down
Horizontal translation left
Horizontal translation right
Reflection over the x-axis
What will be the vertex of
f(x) = 4 (x-3)2 + 1 ?
(3,1)
(1,3)
(-3,1)
(3, -1)
None of these.
Let the graph of g be a translation 2 units down and 4 units left of the graph of f(x) = x2. Write a rule for g.
g(x) = (x - 4)2 - 2
g(x) = (x + 4)2 - 2
g(x) = (x - 4)2 + 2
g(x) = (x + 4)2 + 2
Let the graph of g be a vertical stretch by a factor of 5 of the graph of f(x) = x2. Write a rule for g.
g(x) = 5x2
g(x) = -5x2
g(x) = x2 + 5
g(x) = (x + 5)2
Let the graph of g be a translation 7 units right and a reflection in the x-axis of the graph of f(x) = x2. Write a rule for g.
g(x) = -(x - 7)2
g(x) = (x - 7)2
g(x) = -(x + 7)2
g(x) = (x + 7)2
Let the graph of g be a translation 7 units right and 12 units up of the graph of f(x) = (x + 3)2 - 8. Write a rule for g.
g(x) = (x - 4)2 + 4
g(x) = (x + 10)2 + 4
g(x) = (x - 4)2 - 20
g(x) = (x + 10)2 - 20
Let the graph of g be a reflection in the x-axis of the graph of f(x) = x2 - 7. Write a rule for g.
g(x) = x2 + 7
g(x) = -x2 + 7
g(x) = -x2 - 7
g(x) = -7x2
Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the x-axis of the graph of f(x) = x2 + 2. Write a rule for g.
g(x) = 3x2 + 6
g(x) = -3x2 - 6
g(x) = -3x2 - 2
g(x) = 3x2 + 2
For g(x) = (x - 10)2 - 4, describe the transformation from the parent function.
Shift left 10 and down 4 units
Shift right 10 and down 4 units
Shift left 10 and up 4 units
Shift right 10 and up 4 units
For g(x) = 2(x + 3)2, describe the transformation from the parent function.
Vertical stretch by factor of 2, slide left 3 units
Vertical stretch by factor of 2, slide right 3 units
Slide up 2 units and left 3 units
Slide up 2 units and right 3 units
For g(x) = -x2 +13, describe the transformation from the parent function.
Reflection in x-axis, slide up 13 units
Reflection in x-axis, slide down 13 units
Slide up 13 units
Slide down 13 units
For g(x) = -3(x - 6)2 + 2, choose the transformation from the parent function that does NOT occur.
Reflection in the x-axis
Vertical stretch by factor of 3
Slide 6 units left
Slide 2 units up
The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.
g(x) is shifted up 6 units
g(x) is shifted down 6 units
g(x) is shifted left 6 units
g(x) is shifted right 6 units
Which transformation will occur if f(x) = x is replaced with 41f(x) ?
Vertical stretch by a factor of 4
Vertical compression by a factor of 1/4
Vertical translation up by 1/4 units.
Horizontal compression by a factor of 1/4
What is the linear parent function?
y = x
y = mx + b
f(x) = 2x
Not here
down, which of the following equations would the new graphed
line represent?
Which of the following g(x) equations is vertically stretched and shifted down from f(x) = x?
g(x) = 2 f(x) + 6
g(x) = 1/2 f(x) + 6
g(x) = 2 f(x) - 6
g(x) = 1/2 f(x) - 6
The linear parent function, f(x) = x, is transformed to g(x) = f(x) + 3. Describe the transformation.
g(x) is shifted up 3 units
g(x) is shifted down 3 units
g(x) is shifted left 3 units
g(x) is shifted right 3 units
Which transformation on
f(x) = x
is g(x) = -f(x)
Reflection across the y-axis
The slope will be less steep
The graph will be wider
Reflection across the x-axis.
Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
Graph g shifted down 3 units
Graph g shifted down 4 units
Graph g shifted up 4 units
Graph g reflected
Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
Graph g shifted down 6 units
Graph g is steeper by a factor of 7
Graph g is less steep by a factor of 1/3
Graph g shifted up 6 units
Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
Graph g reflected
Graph g shifted up 2 units
Graph g reflected and shifted down 2 units.
Graph g reflected and shifted up 2 units
f(x) = x2 to the graph of g(x) = (x + 4)2?
Moves up 2
Moves left 4
Moves right 7
Moves down 1
Moves right 1
If the blue is f(x)=x2, then the red must be
If f(x) is the red graph and g(x) is the blue graph, what transformation changes f(x) to g(x)?
translation
rotation
reflection
vertical stretch
Which function DOES NOT represent a horizontal shift of the function f(x)=x2
g(x)= x2+3
g(x)= (x+3)2
g(x)= (x-3)2
g(x) =(x-2)2
Where is the vertex of y=3(x−26)2+14 ?
(26, 14)
(14, 26)
(-26, 14)
(3, 14)
(3, 26)
What does the transformation f(x) → f(x+1)−9 do to the graph of f(x) ?
translates it left one unit and down 9 units
translates it right one unit and down 9 units
translates it up one unit and right 9 units
translates it down one unit and left 9 units
The linear parent function, f(x) = x, is transformed to g(x) = f(x + 3). Describe the transformation.
g(x) is shifted up 3 units
g(x) is shifted down 3 units
g(x) is shifted left 3 units
g(x) is shifted right 3 units
Identify the vertex of f(x) = -2(x+1)2 + 3
(h,k)
(3, 1)
(-1,-3)
(-1,3)
What steps transform the graph y = x2 to y = 2(x+2)2 - 5?
Compress by 2, shifted 2 units left and 5 down
Stretch by 5, shifted 5 units left and 2 down
Stretch by 2, shifted 2 units left and 5 down
Compress by 5, shifted 2 units left and 2 down
What steps transform the graph y = x2 to y = (x-4)2
Shifted down 4 units
Shifted left 4 units
Shifted right 4 units
Shifted up 4 units
Given f(x) = ax² , if 0 < a < 1 , the graph will transform by
becoming wider or vertically compressed
becoming narrower or vertically stretched
Given f(x) = ax² , if a > 1 , the graph will transform by
becoming wider or vertically compressed
becoming narrower or vertically stretched
In the vertex form f(x) = a(x - h)² + k , what does the 'h' value do?
Shifts the function left or right
Reflection over the x-axis
Vertical stretch or compression
Shifts the function up or down
y = x2 + 2
How did we transform from y=x2?
y = -3x2
vertical reflection and vertical shift down
vertical reflection and vertical stretch
horizontal stretch
vertical reflection and vertical compression
Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?
Horizontal shift left 6, vertical shift up 2
Horizontal shift left 6, vertical shift down 2
Horizontal shift right 6, vertical shift down 2
Horizontal shift right 6, vertical shift up 2
