What is the range of a function like #f(x)=5x^2#?

Answer 1

The range of #f(x) = 5x^2# is all real numbers #>= 0#

The range of a function is the set of all possible outputs of that function.

To find the range of this function, we can either graph it, or we can plug in some numbers for #x# to see what the lowest #y# value we get is.

Let's plug in numbers first:

If #x = -2#: #y = 5 * (-2)^2#, #y = 20#
If #x = -1#: #y = 5 * (-1)^2#, #y = 5#
If #x = 0#: #y = 5 * (0)^2#, #y = 0#
If #x = 1#: #y = 5 * (1)^2#, #y = 5#
If #x = 2#: #y = 5 * (2)^2#, #y = 20#

The lowest number is 0. Therefore the y value for this function can be any number greater than 0.

We can see this more clearly if we graph the function:

The lowest value of y is 0, therefore the range is all real numbers #>= 0#

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Answer 2

Chloe Alexander

The range of the function ( f(x) = 5x^2 ) is all real numbers greater than or equal to zero, denoted as ( [0, +\infty) ). This is because when you square any real number, the result is always non-negative (zero or positive). Therefore, the function ( f(x) = 5x^2 ) outputs values that are all non-negative real numbers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.