NAME______________________
Lesson 2 - Transformations—Steepness
Transformations
Graph the following functions on desmos:
f1(x) = 2x
f2(x) = 5x
f3(x) = 0.5x
f4(x) = 0.1x
How does f2 compare to f1?
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How does f3 compare to f1?
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How does f4 compare to f1?
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What if we add some negative signs...how will this affect the steepness??
f1(x) = 2x
f2(x) = -2x
f3(x) = -0.5x
f4(x) = -5x
How does f2 compare to f1?
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How does f3 compare to f1?
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How does f4 compare to f1?
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When looking for the change in a function’s steepness, look at the
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What about steepness of a quadratic function?
f1(x) = x2
f2(x) = 2x2
f3(x) = 0.5x2
f4(x) = -5x2
How does f2 compare to f1?
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How does f3 compare to f1?
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How does f4 compare to f1?
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Write an equation that is WIDER/LESS STEEP than the function f(x) = x2: __________________
Write an equation that is WIDER/LESS STEEP than the function f(x) = 3x2: _________________
Write an equation that is NARROWER/MORE STEEP than the function f(x) = 3x2: _________________
Practice!
#1) Given the equation y = 2|x|, write an equation whose graph is more steep and reflected.
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#2) Given the equation y = -3x + 4, write an equation whose graph is less steep.
#3) Given the equation y = .5x2, write an equation whose graph is less steep and reflected
#4) Given the equation y = 4x, write an equation whose graph is more steep and reflected across the y axis
More Practice:
REMEMBER: When looking for the change in a function's steepness, look at the
absolute value of the leading coefficient.
General Rules:
1. 𝑦 = 5𝑥 and 𝑦 = −5𝑥 have the same steepness Explain why_______________________
2. y = −5𝑥 is more steep than y = 2x Explain why_______________________
3. 𝑓(𝑥) = −0.5𝑥 + 2 is less steep than 𝑔(𝑥) = −0.75𝑥 – 1
Explain
why_______________________
Linear Functions: - each group member should have a different answer for examples
1. Write an equation that is LESS STEEP than the function f(x) = 7x
___________________________
2. Write an equation that is MORE STEEP than the function f(x) = .25x
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Quadratic Functions: : - each group member should have a different answer for examples
3. Write an equation that is WIDER/LESS STEEP than the function f(x) = x2:
_____________________
4. Write an equation that is WIDER/LESS STEEP than the function f(x) = 4x2: _____________________
5. Write an equation that is NARROWER/MORE STEEP than the function f(x) = 7x2: ________________
6. Write the “rule” for the steepness of a quadratic: __________________________________________
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Exponential Functions: - each group member should have a different answer for examples
3. Write an equation that is WIDER/LESS STEEP than the function f(x) = 2x:
_____________________
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4. Write an equation that is WIDER/LESS STEEP than the function f(x) =( )2x: __________________
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5. Write an equation that is NARROWER/MORE STEEP than the function f(x) = (3)2x: ______________
6. Write the “rule” for the steepness of an exponential: _______________________________________
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Absolute Value Functions:
7. Write an equation that is WIDER/LESS STEEP than the function f(x) = |3x| _____________________
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8. Write an equation that is NARROWER/MORE STEEP than the function f(x) =| 𝑥|_______________
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9. How are the “rules” for absolute value and quadratic similar? ________________________________
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REVIEW:
10. Given y = 4x – 5, write an equation whose graph is reflected and shifted up 6 units.
11. Given y = x – 2, write an equation whose graph is less steep and shifted up 8 units.
12. Given:
Function 1 y = - x2 – 4
and
Function 2 y = - 3x2 + 2, complete the following sentence
(circle the appropriate words and fill in the blank):
The graph of Function 2 is less steep / more steep than the graph of function 2,
and is shifted up / down _________ units.
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