Http://lbcsd.innersync.com/sites/jhayes/documents/U1M3Gr6pg.49-502015JHayes.pdf
Answer:
g(x) = (x-3)³ is the transformed function.
Step-by-step explanation:
Horizontal shift:
If f(x) is the parent function.
Then horizontal shift can be expressed as:
, will shift left units.
, will shift 
right c units.
Given the parent function
f(x) = x³
From the graph, it is clear that the transformed function is indicating that the parent function has been horizontally shifted right 3 units.
Therefore, according to the rule, :
g(x) = (x-3)³ is the transformed function.
From the graph,
- The Red graph indicates the parent function i.e. f(x) = x³
- The Blue graph indicates the transformed function i.e. g(x) = (x-3)³
It is clear that the blue graph is obtained when the parent function has been horizontally shifted right 3 units.
Therefore, g(x) = (x-3)³ is the transformed function.
Answer:
$6.21
Step-by-step explanation:
1 apple = $0.60
3 apples = $1.80 (Multiply 0.60 by 3)
2 bananas = $1.00 (Multiply 0.50 by 2)
1 quart of yoghurt = $4.50
Add the prices up first:
1.80 + 1.00 + 4.50 = $7.30
7.30 off 15% = $6.21
The required plane Π contains the line
L: (-1,1,2)+t(7,6,2)
means that Π is perpendicular to the direction vector of the line L, namely
vl=<7,6,2>
It is also required that Π be perpendicular to the plane
Π 1 : 5y-7z+8=0
means that Π is also perpendicular to the normal vector of the given plane, vp=<0,5,-7>.
Thus the normal vector of the required plane, Π can be obtained by the cross product of vl and vp, or vl x vp:
i j k
7 6 2
0 5 -7
=<-42-10, 0+49, 35-0>
=<-52, 49, 35>
which is the normal vector of Π
Since Π has to contain the line, it must pass through the point (-1,1,2), so the equation of the plane is
Π : -52(x-(-1))+49(y-1)+35(z-2)=0
=>
Π : -52x+49y+35z = 171
Check that normal vector of plane is orthogonal to line direction vector
<-52,49,35>.<7,6,2>
=-364+294+70
=0 ok
