Find the value of k that makes f(x) continuous at x= –
1

(Show your work please.)
Giving out brainliest. And 23 points.

5

Step-by-step explanation:

Since, the function f(x) is continuous at x=3.

Therefore,

· k=lim

x→ 3

· x−3

(x+3)

2

−36

· k=lim

x→ 3

· x−3

(x+3)

2

−6

2

· k=lim

x→ 3

· x−3

(x+3−6)(x+3+6)

· k=lim

x→ 3

· x−3

(x−3)(x+9)

· k=lim

x→ 3

· (x+9)

k=3+9=12

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: