Mr. Simonds MTH 95 โ Week 1 Extension Solutions
Page 1 of 2
1. The line passes through the points
(
)
8,2 and
(
)
2,7โ, so its slope is 72 1
28 2
mโ
=
=โ
โโ .
We now know half of the formula:
()
1
2
gx x b
=
โ+
.
Using the fact that
()
82g= gives us
()
182 6
2bb
โ
+= โ =.
So the function is
()
16
2
gx x=โ + .
Please note that the other point checks:
() ()
1
226
2
7
g
โ
=โ โ +
=
2. a.
()()
44 412
41612
44
fx x
x
x
+= +โ
=+โ
=+
b.
(
)
44 124
48
fx x
x
+
=โ+
=โ
c.
()()( )
(
)
444412
44412
16
fx fx x x
xx
+โ = +โ โ
=+โ+
=
d. 4120
412
3
t
t
t
โ=
=
=
The only zero of
f
is 3.
e.
() ()
10 4 10 12
28
f=โ
=
f. 41248
460
15
t
t
t
โ=
=
=
The function value equals 48 at 15.
g.
The t-intercept is
()
3,0 (See part d.)
Since
()
012f=โ , the y-intercept is
(
)
0,12
h.
()
40
412 40
428
7
ft
t
t
t
>โ
โ>โ
>โ
>โ
()
40ft>โ at every value of t on
(
)
7,
โ
โ.
