Question

What is the range of the graphed function?

{x |1< x < 5)
y
x
y

Answer 1

Please check the explanation.

Explanation:

Given the expression

`V=\sqrt[3]{x-1}+3`

Determining the domain:

We know that the domain of a function is the set of input values for which the function is defined.

From the given graph, it is clear that the function has no undefined points nor domain constraints.

Therefore, the domain is:

• x is a real number

In other words:

`\mathrm{Domain\:of\:}\:\sqrt[3]{x-1}+3\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}`

Determining the range:

We know that the range of a function is the set of values of the dependent variable for which a function is defined.

It is clear from the graph that the range can be any real number.

i.e. the range is:

y

In other words,

`\mathrm{Range\:of\:}\sqrt[3]{x-1}+3:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}`