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Chapter 1: Problem 65

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y=x \sqrt{x+6}$$

Short Answer

Expert verified
The function \(y = x \sqrt{x+6}\) has one intercept at (0,0).

Step by step solution

01

Determine X-intercepts

When y = 0, solve the equation \(0 = x \sqrt{x+6}\). This either implies x = 0, or \(\sqrt{x+6} = 0\), which further leads to \(x = -6\). Note, since x should be greater or equal to -6 as it is in the domain of \(sqrt{x+6}\), only x = 0 is valid.
02

Determine Y-intercept

The y-intercept is found when x = 0. Plug x = 0 in the equation, yield \(y = 0* \sqrt{0+6}\), which gives y = 0.
03

Plot the Function and Intercepts

Plot the function \(y = x \sqrt{x+6}\) using a graphing utility. Make sure to mark the intercepts found in the previous steps (0,0). The function increases gradually after x = 0.

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