Algebra 2/Trig 2.7 Transformations
Parent Functions
Function
Name
p. 133
Picture
f(x) = x
f(x) = x2
f(x) = |𝑥|
f(x) = 2x
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f(x) = 𝑥
We can translate, stretch/compress, and reflect the graph of the
parent function.
Horizontal and Vertical Translations (shifts)
Working with f(x) = x2, graph the parent function:
What do we have to do to the equation
to move the graph up 3 units?
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What does the equation look like?
Graph the new function with the parent function.
Describe this transformation.
Does this transformation change the shape of the graph?
How would we move the graph down?
How do we move the graph side-to-side? (Horizontally)
Graph f(x) = x2.
f(x) = (x – 2)2 This will produce a horizontal shift.
Describe the transformation.
This follows the equation f(x) = (x – h)2. What values of h will shift the
graph to the left?
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What values of h will shift the graph to the right?
If the number is placed inside the ( ), it will shift the graph
______________________________.
If the number is outside the ( ), it will shift the graph
___________________________________.
EX) f(x) = (x + 2)2 results in a __________________________ shift
_____ units to the ____________.
f(x) = (x – 3)2 results in a __________________________ shift
_____ units to the ____________.
Describe the transformation that takes place for the given equation:
f(x) = (x + 4)2 – 1.
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Stretches and Compressions
Graph f(x) = x2.
Graph f(x) = 2x2. How did the graph change?
Describe the transformation.
What will happen to the graph of f(x) = x2 if the coefficient (a) is less
than 1, greater than 0?
Graph f(x) = ½x2. (This is of the form f(x) = ax2).
Describe the transformation.
To make the parent function narrower – a stretch, “a” must be
________________________________.
To make the parent function wider – a compression, “a” must be
______________________________.
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Ex.) f(x) = 3x2, will this produce a stretch or a compression?
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If f(x) = 3x2, will this produce a stretch or a compression? (We
consider multiplying by 1/3 the same as dividing by 3.)
Multiplying or dividing our parent function produces a
________________ or a ____________________.
Reflection:
f(x) = -x2. What does the negative sign our front do to the graph of
f(x) = x2?
Draw the graph of f(x) = -x2.
This is called a ____________________________ reflection over the
x-axis.
Given: f(x) = -4(x – 3)2 + 2. Describe this transformation.
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How do we reflect horizontally? (over the y-axis)
Graph f(x) = -4(-3x – 2)2 + 2. Describe this transformation.
A _____________________________ compression is the same as a
_______________________ stretch.
HW p. 139 – 140. Problems 12 – 56 EVENS (23 problems)
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