Question

Which function has a range limited to only negative numbers?

Answer 1

F(x)=-x^2

Explanation:

The one example of function with range of only negative number is:

F(x)=-x^2

Why this? We know for every x, x^2 is positive. So -x^2 will be negative.

Answer 2

The function in the given image that has a range limited to only negative numbers is
`y = -x^2`.

The range of a function is the set of all possible output values that the function can produce. For a function y = f(x), the range is defined as the set of all y-values such that there exists an x-value for which f(x) = y.

The function
`y = -x^2` is a quadratic function, which means that its graph is a parabola. The parabola opens downwards, which means that all of its y-values are negative. Therefore, the range of the function is limited to only negative numbers.

To see this mathematically, note that the equation
`y = -x^2` can be rewritten as
`y = -(x^2)`. The square of any real number is always non-negative, so
`-(x^2)` must always be negative. Therefore, the range of the function is limited to only negative numbers.

Here are some examples of input and output values for the function
`y = -x^2`

Input (x) Output (y)

-2 4

-1 1

0 0

1 -1

2 -4

As you can see, all of the output values are negative. Therefore, the range of the function is limited to only negative numbers.