How do you determine the domain of a function ?

Let y = f(x) be a function with an independent variable x and a dependent variable y.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that

chosen x-value is said to belong to the domain of f. If there is a requirement that a y-value produced by a function

must be a real number, the following conditions are commonly checked:

1. Denominators cannot equal 0.

2. Radicands (expressions under a radical symbol) of even roots (square roots, etc)  

cannot have a negative value.

3. Logarithms can only be taken of positive values.

4. In word problems physical or other real-life restrictions might be imposed, e.g. time is  

nonnegative, number of items is a nonnegative integer, etc.

the domain is a set of all possible numbers inputs for that function, THe range is all the possible output numbers

i hope this helps

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

answer: 2 and 1

step-by-step explanation: got this question