<h2>
Answer:</h2>
Ques 1)
Ques 2)
<h2>
Step-by-step explanation:</h2>
Ques 1)
We know that if a graph is stretched by a factor of a then the transformation if given by:
f(x) → a f(x)
Also, we know that the translation of a function k units to the right or to the left is given by:
f(x) → f(x+k)
where if k>0 then the shift is k units to the left
and if k<0 then the shift is k units to the right.
Here the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
This means that the function g(x) is given by:
Ques 2)
We know that the transformation of the type:
f(x) → f(x)+k
is a shift or translation of the function k units up or down depending on k.
If k>0 then the shift is k units up.
and if k<0 then the shift is k units down.
Here, The graph of the function f(x)=|3x| is translated 4 units up.
This means that the transformed function g(x) is given by:
First thing to do is to illustrate the problem, Since it was mentioned that work was along the way to training, the order is shown in the picture. Mary's home and workplace are nearer compared to her training center. It is also mentioned that the distance between work and home, denoted as x, is 2/3 of the total distance from home to training. The total distance is (x + 2.5). Thus,
x = 2/3(x+2.5)
x = 2/3 x + 5/3
1/3 x = 5/3
x = 5 km
Thus, the distance from home to work is 5 km. This means that Mary has to walk this distance twice to return home to get her shoes. Then, she will travel again the total distance of 5+2.5 = 7.5 km to get to her training center. So,
Total distance = 2(5km) + 7.5 km
Total distance = 17.5 km
Choices:
(7, 44)
(8, 48)
(9, 52)
(12, 74)
<span>(13, 78)
r = 6t
(7,44) : r = 6(7) = 42 incorrect
(8,48) : r = 6(8) = 48 CORRECT
(9,52) : r = 6(9) = 54 incorrect
(12,74) : r = 6(12) = 72 incorrect
(13,78) : r = 6(13) = 78 CORRECT
The points that lie on the resulting line are (8,48) and (13,78)</span>
3000000...........
10^6 =1000000 (3) = 3000000
