Answer: Domain is All Real Numbers, Range is All Real Numbers
Step-by-step 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:
[tex]\begin {array}{c|l}\underline{\quad x \quad }&\underline{y=2\sqrt[3]{x} +1}\\ -8&-3\\-1&-1\\ \ 0&\ 1\\ \ 1&\ 3\\ \ 8&\ 5\\\end{array}[/tex]
