HOMEWORK I : RIGID TRANSFORMATION
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2 Plot the Parent Function and graph the required transformation. Make sure to label at least 3 points on
the final graph.
a. 𝑓(𝑥) = √−𝑥 + 2 − 1
b.𝑓(𝑥) = − (𝑥 − 2)3 + 3
3. The graph of 𝑦 = 𝑓(𝑥) passes through the given
points (0,1) , (1,2) and (2,3). Find the corresponding
points on the graph of:
c. 𝑓(𝑥) = −(𝑥 − 3)2 − 2
4. The graph of ℎ(𝑥) passes through ( -4,2). Find the
corresponding point on the graph of:
a. 𝑦 = −2ℎ(𝑥 + 1 ) − 3
a. 𝑦 = −𝑓(𝑥 + 2) − 1
b. 𝑦 = 𝑓(2 − 𝑥) + 3
b. 𝑦 = −ℎ(2𝑥 − 1) + 1
c. 𝑦 = −𝑓(−𝑥 − 1) − 5
5. Name the Parent and describe all its
transformations. Do not graph:
a. 𝑓(𝑥) = − √−𝑥 + 1 + 3
6. Given a description of its transformation, give the
new equation.
a. 𝑃𝐹: √𝑥 , reflection across the x-axis, shift 3 units
left and 2 units up, reflects across the y-axis.
b. ℎ(𝑥) = |1 − 𝑥| − 4
b. 𝑃𝐹: 𝑥 3 , shift 3 unit right and 1 unit down, reflects
across the y-axis.
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HW 2 NONRIGID TRANSFORMATION:
A. Describe all the transformation in each of the
following functions( Identify each Parent Function.
1. ℎ(𝑥) = 2 log(−𝑥 + 3) − 5
B. Find the function that is finally graphed after the
following transformations are applied to the given
parent function (PF)
6. PF: 𝑦 = log 𝑥
5. PF : 𝑦 = 3√𝑥
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2 𝑓(𝑥) = − 2 (𝑥 − 4)3 + 1
3. 𝑝(𝑥) = −√10 − 2𝑥 − 3
3
…Shift 3 units left
…Shift 2 units up
…Vertically compressed
by a factor of ½
…reflects across x-axis
…reflects across y-axis
…Shift 1 unit left
…Shift 4 units down
…Horizontally stretched
by a factor of 4
…Reflects across y-axis
…Vert. stretched by 3
7. PF: 𝑦 = 𝑒 𝑥
8. PF: 𝑦 = |𝑥|
…Hor. Stretched by 3
…Shift 1 unit down
…shift right 1 unit
…Vert. comp. by 1/3
…Reflects across y-axis
…reflects across x-axis
…Vertically stretch by a
factor of 2
…Horizontally comressed by a factor of ½
…Reflects across y-axis
…Shift 2 units up
…Shift 1 left
4. 𝑣(𝑥) = −2 √( 5 − 𝑥) − 6
5. ℎ(𝑥) = 0.2 |−3𝑥 − 6| + 1
9. If (-8,6) is on the graph of 𝑦 = ℎ(𝑥), what is the corresponding point on the graph of
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𝑎) 𝑦 = − 2 ℎ(3 − 2𝑥)+1?
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b) 𝑦 = 3ℎ (− 2 (𝑥 − 1)) − 3?
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c)𝑦 = 3 ℎ(−3𝑥 + 6) − 2
10. Plot the PF and sketch according to the required transformation. Clearly label at least 3 points of the
final graph.
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1
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𝑏. 𝑓(𝑥) = 2 √𝑥 + 1 − 3
𝑐. ℎ(𝑥) = − |6 − 3𝑥| + 1
(𝑥
a. ℎ(𝑥) = −3 √− 2 − 1) + 4
2
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d. 𝑓(𝑥) = − 𝑥+1 − 3
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e. ℎ(𝑥) = −2 |2 (𝑥 − 6)| + 1
𝑓. ℎ(𝑥) = −2 (3 − 𝑥)2 − 1
Classwork NON-RIGID TRANSFORMATION CLASSWORK ( Please make a copy of this before our class)
on October 15, 2020 (A Day) and October 16 (B Day)
A
B
C
D
E
F
D
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*** Given that points (-6,-4) and (9,2) are on f(x), what is the new coordinate of 𝑦 = − 2 𝑓( 12 − 3𝑥) + 1?