Even Roots

This course is the study of the real numbers. As a result we don’t take even roots of negative numbers.

Even roots

look a lot like the square root

Their domains do not include negative numbers: \([0, \infty )\). Their domains are the nonnegative numbers. These functions increase very slowly over their domain, becoming unbounded.

The graph of \(y = SR(x) = \sqrt {x}\)

The square root function begins where the inside of the radical equals \(0\). It then moves in the direction that keeps the inside positive.

Even Root

The graph of \(y = f(v) = \sqrt {v+3}\)

Here the inside \(v+3\) equals \(0\) when \(v=\answer {-3}\). That is the start of the domain. Then, the inside is positive \(v+3>0\), when \(v>-3\), which means the graph moves up to the right.

Even Root

The graph of \(y = T(k) = \sqrt {-k+5}\)

Here the inside \(-k+5=0\) equals \(0\) when \(k=\answer {5}\). That is the start of the domain. Then the inside is positive \(-k+5>0\), when \(k\) \(<\) \(>\) \(5\), which means the graph moves up to the left. The domain is \((-\infty ,5]\).

Odd Roots

This course is the study of the real numbers. As a result we don’t take even roots of negative numbers, however we do have odd roots of negative numbers

Odd roots

look a lot like the cube root

Their domains include all real numbers: \((-\infty , \infty )\). Odd root functions increase very slowly over this domain, becoming unbounded.

The graph of \(y = CubeRoot(x) = \sqrt [3]{x}\)

The cube root function has a vertical tangent line where the inside of the radical equals \(0\).

Odd Root

The graph of \(y = f(v) = \sqrt [3]{v+3}\)

Here the inside \(v+3\) equals \(0\) when \(v=\answer {-3}\). The graph has a vertical tangent line there. Otherwise, the cube root function is increasing everywhere, but increasing slower and slower and slower.