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Chapter 1: Problem 72

Graph the function and determine the interval(s) for which \(f(x) \geq 0\). $$ f(x)=\sqrt{x+2} $$

Short Answer

Expert verified
The function \(f(x) = \sqrt{x + 2}\) is greater or equal to zero for the interval \([-2, \infty)\).

Step by step solution

01

Solve the inequality

Begin by setting the body of the square root function, \(x + 2\), to be greater or equal to zero and solve for \(x\). This can be done by subtracting 2 from both sides of the equation. Thus, \(x + 2 \geq 0\) implies that \(x \geq -2\).
02

Sketch the graph

Next, sketch the graph of the function \(f(x) = \sqrt{x + 2}\). This is a square root function that has been horizontally translated 2 units to the left. This means that the vertex (the starting point) of the graph will be at \((-2, 0)\). The graph will remain above or on the x-axis and will increase gradually as \(x\) moves to the right.
03

Identify the intervals

From the graph and the inequality \(x \geq -2\), it is seen that \(f(x) \geq 0\) for all \(x \geq -2\). Hence, the interval for which \(f(x) \geq 0\) is \([-2, \infty)\). This is the final answer.

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Most popular questions from this chapter

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