SME
Grade 11 Math · Problem type
Where a point goes
Use this for “(2, 4) is on y = 2ˣ. Where is it on y = −3 × 2ˣ⁺¹ + 5?”
Chart
Horizontal asymptote y = 5
f(1) = −7
The parent y = 2X is dashed
x on the parent: 2
y on the parent, 2ᵖ: 4
This is an example. Type your own values to start a new problem.
y
=
a
×
2
x
−
(
)
+
k
p
x on the parent
example
q
y on the parent, 2ᵖ
worked out (not typed)
X
x of the moved point
worked out (not typed)
Y
y of the moved point
worked out (not typed)
Formulas
q
=
2
p
4
=
2
2
X
=
p
+
h
1 = 2 + (−1)
Y
=
a
×
q
+
k
−7 = −3 × 4 + 5
Assumptions
•
Horizontal moves change x only: the point (p, 2ᵖ) moves to x = p + h.
•
Vertical moves change y only: the y-value is stretched by a, then moved up k.
•
The asymptote y = 0 moves to y = k.
Step-by-step
WE KNOW
p = 2, a = −3, h = −1, k = 5
FIND
y on the parent, 2ᵖ (q), x of the moved point (X), y of the moved point (Y)
Step 1 · Find y on the parent, 2ᵖ (q)
Use q = 2ᵖ
The point on the parent y = 2ˣ.
q
=
2
2
q
=
4
Step 2 · Find x of the moved point (X)
Use X = p + h
The
shift
right
moves
the
x
of
every
point
by
h
.
X
=
2
−
1
X
=
1
Step 3 · Find y of the moved point (Y)
Use Y = a × q + k
Stretch
the
y
by
a
,
then
move
it
up
by
k
.
Y
=
−3
×
4
+
5
Y
=
−12
+
5
Y
=
−7
Check
Put the numbers back in. Both sides should match.
4
=
2
2
✓
1 = 2 − 1 ✓
−7 = −3 × 4 + 5 ✓
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Parent functions and transformations: shifts, stretches and reflections
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Horizontal stretch and flip
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