Question

The output of a relation is the difference of three times the input and five. Select the correct answer from each drop-down menu. The equation that represents this relation is . The relation a function. If the domain of the relation is x > 2, the range of the relation is y > .

Answer 1

The equation that represents this relation is [ y= 3x - 5 ]

The relation [ is ] a function.

If the domain of the relation is x > 2, the range of the relation is y > [ 1 ].

Explanation:

The output, y, of a relation, is the difference of three times the input, or 3x, and 5. So, y = 3x − 5.

Substituting any x-value from the domain into the equation will result in exactly one value of y, so the relation is a function.

To find the range of the relation, given the domain, substitute the boundary point of the domain into the function equation:

When x = 2, y = 3(2) − 5 = 6 − 5 = 1.

Because substituting values of x that are greater than 2 will result in values of y that are greater than 1, the range of the relation is y > 1.

Hope this helps !!

Answer 2

The equation that represents this relation is
`y = 3x - 5`.

The relation is a function.

If the domain of the relation is x > 2, the range of the relation is
`y >1`

Explanation:

Given

Output = 3 * Input - 5

Required

Complete the gap

Solving (a):The equation for the relation.

Let

`x \to` input

`y \to` output

The relation is:

`y = 3 * x - 5`

`y = 3x - 5`

Solving (b): Is the relation, a function?

Yes; Because every value of x has a distinct value in 7

Solving (c): The range:

Domain:
`x > 2`

Substitute 2 for x in
`y = 3x - 5`

`y =3 * 2 - 5`

`y =6 - 5`

`y =1`

The range is:

`y >1`