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Specimen 2017 H2 Mathematics Paper 1 Question 2
Graphs and Transformations
Answers
(a)
y
=
1
2
(
x
+
2
)
3
+
1.
{y=\frac{1}{2} (x+2)^3 + 1.}
y
=
2
1
(
x
+
2
)
3
+
1.
(b)
x
=
7.722.
{x=7.722.}
x
=
7.722.
Full solutions
(a)
y
=
x
3
y = x^3
y
=
x
3
Replacing
x
{x}
x
with
x
+
2
,
{x+2,}
x
+
2
,
to translate
2
{2}
2
units in the negative
x
-axis
,
{x\textrm{-axis},}
x
-axis
,
y
=
(
x
+
2
)
3
y=(x+2)^3
y
=
(
x
+
2
)
3
Stretch of factor
1
2
{\frac{1}{2}}
2
1
parallel to the
y
-axis
,
{y\textrm{-axis},}
y
-axis
,
y
=
1
2
(
x
+
2
)
3
y=\frac{1}{2} (x+2)^3
y
=
2
1
(
x
+
2
)
3
Translation of
1
{1}
1
unit in the positive
y
-direction
,
{y\textrm{-direction},}
y
-direction
,
y
=
1
2
(
x
+
2
)
3
+
1
■
y=\frac{1}{2} (x+2)^3 + 1 \; \blacksquare
y
=
2
1
(
x
+
2
)
3
+
1
■
(b)
Solving with a GC, at the point where the two curves intersect,
x
=
7.7218
(4 d.p.)
■
{x=7.7218 \textrm{ (4 d.p.)} \; \blacksquare}
x
=
7.7218
(4 d.p.)
■
x
{x}
x
y
{y}
y
(
0
,
0
)
{(0,0)}
(
0
,
0
)
(
0
,
5
)
{(0, 5)}
(
0
,
5
)
(
7.722
,
460.4
)
{(7.722, 460.4)}
(
7.722
,
460.4
)
y
=
f
(
x
)
{y=f(x)}
y
=
f
(
x
)
y
=
x
3
{y=x^3}
y
=
x
3
x
-intercept
{x\textrm{-intercept}}
x
-intercept
of
y
=
f
(
x
)
:
{y=f(x):}
y
=
f
(
x
)
:
(
−
2
3
−
2
,
0
)
{(\sqrt[3]{-2}-2,0)}
(
3
−
2
−
2
,
0
)
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