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Chapter 1: Problem 64

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y=\sqrt[3]{x+1}$$

Short Answer

Expert verified
The graph of the given function \(y=\sqrt[3]{x+1}\) is a cubic root function shifted 1 unit to the left. It intersects the x-axis at x=-1 and the y-axis at y=1.

Step by step solution

01

Understand the equation

The equation to be graphed is \(y=\sqrt[3]{x+1}\). This is a cubic root function, which means it will have an 'S' shape. The '+1' inside the function indicates it shifted 1 unit to the left. The standard form of this equation is \(\sqrt[3]{x}\). We have to consider this while drawing our graph.
02

Use a Graphing Utility

Plot the given equation \(y=\sqrt[3]{x+1}\) in a graphing utility and look for any points where the graph intersects the x-axis and y axis.
03

Approximate Intercepts

For the x-intercept, set y=0 and solve for x. Setting \(y=\sqrt[3]{x+1}\) to 0, we find \(x=-1\). Intuitively, the graph touches the x-axis at x=-1. For the y-intercept, set \(x=0\) and solve for y. Substituting \(x=0\) into the equation, results in \(y=\sqrt[3]{1}\) which is 1. So, the graph cuts the y-axis at \(y=1\).

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