Based on the family the graph below belongs to, which equation could represent the graph?
y=0.6^x- 2
y = 0.6x^2-1
y=-0.6x^3- 1
V = log(x)-2

y=-0.6x^3- 1

Step-by-step explanation:

In the graph, first we must see the points where the line intersects the axis.

We can see that it goes throug the point (0, -1)

Now, of the given options the only two that are 0 when x is -1, are:

f1(x) =y = 0.6*x^2 - 1

f2(x) =y = -0.6x^3 - 1

We also can see that for all the positive values of x, y has a negative value, so let's value bot functions in x = 2, and see what happens.

f1(2) = 0.6*4 - 1 = 1.4

f2(2) = -0.6*8 - 1 = -5.8

so the correct option is

y=-0.6x^3- 1

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: