Find the domain of y=2/3x-1 if the range is {-3, -1, 7, 17}.

Explanation:

First solve for x to get

y = (2/3)x - 1

y+1 = (2/3)x

(2/3)x = y+1

x = (3/2)*(y+1)

Now plug the values given into y. Do so one at a time. Lets plug in y = -3

x = (3/2)*(y+1)

x = (3/2)*(-3+1)

x = 1.5*(-2)

x = -3

So the domain value x = -3 corresponds to the range value y = -3.

Repeat for y = -1

x = (3/2)*(y+1)

x = (3/2)*(-1+1)

x = 1.5*0

x = 0

The domain value x = 0 corresponds to the range value y = -1

Repeat for y = 7

x = (3/2)*(y+1)

x = (3/2)*(7+1)

x = 1.5*8

x = 12

The domain value x = 12 corresponds to the range value y = 7

Repeat for y = 17

x = (3/2)*(y+1)

x = (3/2)*(17+1)

x = 1.5*18

x = 27

The domain value x = 27 corresponds to the range value y = 17

Just as the domain is the x values, the range is the y values. To null out any confusion, "y" is the same as "f(x)", if that is the notation you are using.

For each range value -3, -1, 7, and 17, we will have an x-value. To find the corresponding x to each y-value, we just plug in the range for y, one at a time, and solve for x.

Try it.

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:

3,000,540

step-by-step explanation: