Question

Graph f(x) = 2 3√x +1. Identify the domain and range of the function.

Answer 1

Answer: Domain is All Real Numbers, Range is All Real Numbers

Explanation:

2∛x + 1

Domain is the restriction on the x-value. Since it is a cube root, the radical can be negative so there is no restriction on x.

Range is the restriction on the y-value. Since there is no restriction on x and there is no denominator, there is no restriction on y.

Graph:

Consider the parent graph f(x) = ∛x. The new graph is a stretch of 2 and a vertical shift up 2 units.

If you re not familiar with transformations, you can make a table and plot the points:

`\begin {array}c\underline{\quad x \quad }&\underline{y=2\sqrt[3]{x} +1}\\ -8&-3\\-1&-1\\ \ 0&\ 1\\ \ 1&\ 3\\ \ 8&\ 5\\\end{array}`