Question

The range of which function includes -4?

Answer 1

Answer:

$y=\sqrt x - 5$

Step-by-step explanation:

Given:

The range of the function includes the value '-4'.

The range of a function is the output of the function denoted by the variable 'y'. The input of the function is called the domain and is represented by the variable 'x'.

Here, the 'y' value is -4 which is a negative number.

The last two options given represent a square root function. We know that, the output of a square root function is always a positive number. So, for the last two options the range is always greater than or equal to 0. Thus, these two options are eliminated.

Now, if we consider the second option, let us replace 'y' by -4 and solve for 'x'. This gives,

$-4=\sqrt x + 5\\-4-5=\sqrt x\\\sqrt x= -9$

But, we know that, the result of a square root function is never negative. Therefore, this option is also incorrect.

Hence, only the first function is correct which can verified below.

$y=\sqrt x-5\\-4=\sqrt x-5\\\sqrt x=-4+5\\\sqrt x=1\\x=1$

So, we got a positive result without violating the definition of square root functions.

Therefore, the correct answer is $y=\sqrt x-5$