2 answers:
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We have been given that:
Vector and
.
Component form of a vector implies to write the vector with each individual components.
Now, our vector is given by
Now,
and
Plugging the values of and
, we get:
So, the vector 'e' in its component form is given as:
For the function 1,
To find the equation for this function, first you take any two points and from these points you will find the slope of line and then put it in the equation of line.
(x₁,y₁)=(0,4)
(x₂,y₂)=(1,7)
slope=m=y₂-y₁/x₂-x₁
=7-4/1-0
=3/1
=3
Equation of a line
f(x)=mx+c
where m is the slope and c is the y intercept.
f(x)=3x+4
For the function 2,
As you have given the equation of a function which is
f(x)=-2x+3
you can easily fill the table,
I do it for one value for other values you will do the same procedure.
For x=-2
f(x)=-2(-2)+3
= 7
x f(x)
-----------------
-2 7
-1 5
0 3
1 1
2 -1
For the Function 3,
You can get the values from the graph directly but you can also solve it by finding the equation first and then by putting method you get the value.
Equation of a line
f(x)=mx+c
where m is the slope and c is the y intercept.
m=(y₂-y₁)/(x₂-x₁)
(x₁,y₁)=(0,-3)
(x₂,y₂)=(6,0)
m=(0-(-3))/(6-0)
m=1/2
f(x)=1/2x-3
x f(x)
-----------------
-2 -4
-1 -7/2
0 -3
1 -5/2
2 -2
The graph of function 1 and 2 are attached below.