Worksheet 10 Memo – Functions: Hyperbolas, Parabolas and Exponential Graphs
Grade 10 – Mathematics
1.
a)
and
b)
The graph was reflected about the
and
the graph was shifted down by 1 unit
y-axis or the -axis.
c)
and
The graph becomes thinner
d)
and
The graph becomes fatter.
e)
and
f)
The graph was shifted 4 units down
g)
and
the graph became thinner
h)
The graph was reflected about the y-axis
i)
and
( )
The graph was reflected about the -axis.
and
and
the graph was shifted down 2 units.
j)
and
The graph moves further from the axes.
2.
a)
b)
and
d)
and
e)
f)
and
g)
h)
c)
3.
and
there are no asymptotes
i)
and
j)
and
a)
and
b)
and
c)
and
d)
e)
g)
f)
no axis of symmetry
i)
4.
a)
and
Domain →
b)
Range →
c)
Domain →
Domain →
d)
Domain →
f)
Domain →
h)
Domain →
Domain →
Domain →
Domain →
Range →
j)
Range →
5.
and
Range →
Range →
i)
j)
Range →
Range →
g)
and
Range →
Range →
e)
h)
Domain →
Range →
a)
(0; 0)
b)
(0; 0)
c)
(0; 2)
d)
(0; -1)
6.
a)
(
)
and
(3; 1)
and
…2
…1
Subs 1 into 2
Subs back into 1
( )
b)
(0; 3)
and
(3; 12)
Subs in (3; 12)
( )
c)
(
)
and y =1
Subs in (
)
√
d)
⊥ to
at (2; 4)
Subs in (2; 4)
( )
e)
(-2; -4)
and y = -2
Subs in (-2; -4)
f)
(-2; 7)
(
and
(5; 49)
and
)
( )
…2
…1
Subs 1 into 2
Subs back into 1:
( )
g)
(-5; 3)
and
y=2
Subs in (-5; 3)
h)
(
)
( )
i)
(-5; -21)
and
(0; 4)
Subs in (-5; -21)
(
)
j)
(-4; -17)
(
Subs in (1; -2)
( )
)
(1; -2)
7.
a)
Domain →
b)
Range →
c)
Range →
Domain →
d)
Range →
e)
Domain →
f)
Domain →
h)
a)
Domain →
Range →
Domain →
j)
Range →
8.
Domain →
Range →
Range →
i)
Domain →
Range →
Range →
g)
Domain →
Domain →
Range →
A (-1; 0)
( )
B (0; 2) → y –intercept
(
c=2
)
( )
And
A (-1; 0)
( )
E (0; 5) → y-intercept
(
b=5
)
( )
b)
( )
(
( )
)(
)
→A
( )
C(
)
c)
EB = 5 -2
d)
= 3 units
e)
⊥ to ( )
Subs in D (1; 0)
( )
( )
f)
( )
( )
and
(
)
( ) and ( ) intersect at (
And
( )
( )
(
)(
)
→ D (1; 0).
and
(
)
(
9.
a)
And ( )
( )
Subs in (-3; 0)
( )
Subs in (-3; 0)
)
( )
( )
( )
( )
(
)(
(B)
)
(0; 3)
( )
(
b)
)
)
and
A (1; 4)
c)
d)
and
e)
Subs in (-1; 0)
( )
f)
g)
The line in question e is one of the axes of symmetry for the function of
( )
( )
√
√
( ) intersects
Or
( ) at the points (√
√
√ ) and ( √
√ ).
( )