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Chapter 1: Problem 67

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y=|x+3|$$

Short Answer

Expert verified
The graph of the function \(y = |x + 3|\) will look like a 'V' with the vertex at \((-3,0)\). And, it intersects the x-axis at \(x = -3\). There is no y-intercept.

Step by step solution

01

Understanding the absolute value function

The absolute value function takes the form \(y = |x - h| + k\), where \(h\) and \(k\) are the coordinates of the vertex of the graph. In this case, the equation is \(y = |x + 3|\), so \(h = -3\) and \(k = 0\). The vertex of the graph is thus at \((-3,0)\).
02

Graphing the function

Using a graphing utility and your determination of the vertex, graph the absolute value function \(y = |x + 3|\), which will look like a 'V'. The vertex of will be at the point \((-3,0)\). The graph opens upwards as there is no negative sign in front of the absolute value bars.
03

Approximate any intercepts

The intercept is the point where the graph crosses the x-axis. From the graph, we can see that the curve intersects the x-axis at \(x = -3\). Therefore, the x-intercept is \(x = -3\). It does not cross the y-axis so no y-intercept exists for this equation.

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