For each relation below, describe the domain and range and determine whether or not the relation is a function.3x-4y=17and x=vy-4

Question

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The second equation is x=√y-4

Answer 1

1.      3x - 4y = 17

To determine the domain and range of this relation, we need to solve for either x or y in terms of the other variable. Let's solve for y:

3x - 4y = 17

-4y = -3x + 17

y = (3/4)x - (17/4)

So the domain is all real numbers and the range is all real numbers. To determine if the relation is a function, we need to check if there is only one output (y) for each input (x). Since we have solved for y in terms of x, this relation is a function.

2.      x = √(y - 4)

Similarly, let's solve for y:

x = √(y - 4)

x^2 = y - 4

y = x^2 + 4

The domain is all real numbers, since any value of x can be squared and then have 4 added to it. The range is all real numbers greater than or equal to 4, since x^2 will always be greater than or equal to 0, and adding 4 to it will result in a value that is greater than or equal to 4. To determine if the relation is a function, we need to check if there is only one output (x) for each input (y). Since we have solved for y in terms of x, this relation is a function.