SME
Grade 11 Math · Problem type
Horizontal stretch and flip
Use this for “(4, 2) is on y = √x. Where is it on y = √(2x)? On y = √(−x)?”
Chart
f(2) = 2
b = 2: the graph is squeezed toward the y-axis to 1/2 of its width
The parent y = √x is dashed
This is an example. Type your own values to start a new problem.
y
=
(x
−
)
p
x on the parent
example
Y
y of the point, √p
worked out (not typed)
X
x of the moved point
worked out (not typed)
Formulas
Y
=
√
p
2
=
√
4
X
=
h
+
p
b
2
=
0
+
4
2
Assumptions
•
Here f(x) = √x, dashed. A number b inside, f(b(x − h)), acts on x: the graph is squeezed toward x = h by 1/b.
•
A b between −1 and 1 stretches the graph instead, and a negative b also flips it across x = h.
•
The parent’s point (p, √p) lands at (h + p ÷ b, √p): only x changes.
Step-by-step
WE KNOW
b = 2, h = 0, p = 4
FIND
y of the point, √p (Y), x of the moved point (X)
Step 1 · Find y of the point, √p (Y)
Use Y = √p
The
point
on
the
parent
is
(
p
,
√
p
);
a
change
inside
the
root
leaves
y
alone.
Y
=
√
4
Y
=
2
Step 2 · Find x of the moved point (X)
Use X = h + p ÷ b
The
new
graph
reads
the
root
of
b
(
X
−
h
),
which
must
be
p
:
so
X
−
h
=
p
b
.
X
=
0
+
4
2
X
=
2
Check
Put the numbers back in. Both sides should match.
2
=
√
4
✓
2
=
0
+
4
2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.