Which is the correct piecewise definition for the function |x−3|=y−1? a. y=−x+2 for x≥−3 and y=x−4 for x< −3 b. y=x−2 for x≥3 and y=−x+4 for x< 3 c. y=x−2 for x< 3 and y=−x+4 for x≥3 d. y=−x+2 for x< −3 and y=x−4 for x≥−3

B. y=x−2 for x≥3 and y=−x+4 for x<3

Answer choices B and C are the only ones with the breakpoint at x=3, where the absolute value function has an argument of zero.

Of those, answer choice B is the only one with a positive slope for x > 3, so is the only correct choice.

B.

Step-by-step explanation:

Given function

We know that the break of modulus function

f(x)=

f(x)

= x-1 for

And

Therefore, similarly we break the modulus function in the same way

we can write as

Therefore , ( by using subtraction property of equality )

And

We can write as (By simplication)

Hence, B. is correct option .

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:

answer: 1 and 3

step-by-step explanation: