Question

The function f(x)=/-x is shown on the graph

Which statement is correct?
A)The range of the graph is all real numbers less than or equal to 0.
BThe domain of the graph is all real numbers less than or equal to 0.
C)The domain and range of the graph are the same.
D)The range of the graph is all real numbers.

Answer 1

The domain of the graph is all real numbers less than or equal to 0.

Explanation:

Given :
`f(x) = -x`

To Find: which statement is correct?

Solution:

Domain : The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

Range : The range is the resulting y-values we get after substituting all the possible x-values.

The function shown on the graph

The domain is the interval :(-∞,0]

`x\leq0`

So, Domain of
`f(x) = -x` : All real numbers less than or equal to zero

The range is the interval: [0,∞)

`y\geq 0`

So,Range of
`f(x) = -x`:All real numbers greater than equal to 0 .

Thus Option B is correct.

The domain of the graph is all real numbers less than or equal to 0.

Answer 2

we know that

For the function shown on the graph

The domain is the interval--------> (-∞,0]

`x\leq0`

All real numbers less than or equal to zero

The range is the interval--------> [0,∞)

`y\geq 0`

All real numbers greater than or equal to zero

so

Statements

case A) The range of the graph is all real numbers less than or equal to
`0`

The statement is False

Because the range is all numbers greater than or equal to zero

case B) The domain of the graph is all real numbers less than or equal to
`0`

The statement is True

See the procedure

case C) The domain and range of the graph are the same

The statement is False

Because the domain is all real numbers less than or equal to zero and the range is is all numbers greater than or equal to zero

case D) The range of the graph is all real numbers

The statement is False

Because the range is all numbers greater than or equal to zero

therefore

the answer is

The domain of the graph is all real numbers less than or equal to
`0`