Desklib Study Material and Solutions

Question 1
B and C
Question 2
a) (-3, 2)
b) The ̊Equationis givenby ( x−h )2+ ( y −k )2=r2
Where ( h , k ) is the center of the circe , r is the radius of the ̊¿ ( x , y ) is a point on the ̊.
Therefore ,
(−1+3 )2 + ( 10−2 )2=r2
r2=4+ 64=68
r = √68= √4∗17
¿ 2 √17
Question 3
a) The x-intercepts are -1,1, and 5
b) The y-intercepts is -3
c) [-1,6]
d) [-3,2]
Question 4
a) f (−2 )= −2+5
(−2−8 ) 2 = 3
100
b) (−∞ , 8 ) U ( 8 , ∞ )
c) f ( a+7 ) = ( a+ 7 ) +5
( ( a+7 ) −8 )2 = a +12
( a−1 )2 = a+ 12
a2 −2 a+1
Question 5
The domain of the quotient function is (−∞ ,−7 ) ∪ (−7 , ∞ ). The domain of the quotient function is
only influenced by the nature of the denominator function. Given that we take absolute values of the
denominator, we can have both negative values as long as the function is defined. However, for negative
infinity, infinity and -7, the quotient function is undefined. Thus we exclude them from the domain.
Question 6
a) $6300 lies in the second bracket. Therefore,
T ( 6300 )=70+0.035 ( 6300−2500 )=$ 203
b) $63000 lies in the third bracket, so
T ( 63000 ) =245+0.05 ( x−7500 )
¿ 245+0.05∗55500
¿ $ 3020

Question 7
a) At x−intercepts, y=0 ,
Therefore 2−2 x2=0
2 x2=2 x2=1 ,
Thus x=1∨−1
Therefore x−intercepts are 1∧−1
b) At y intercept , x=0.
Therefore y=2−2∗0=2
Therefore y−intercept is 2.
c)
x y (x, y)
-3 -16 (-3,-16)
-2 -6 (-2,-6)
-1 0 (-1,0)
0 2 (0,2)
1 0 (-1,0)
2 -6 (2,-6)