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Chapter 1: Problem 71

Graph the function and determine the interval(s) for which \(f(x) \geq 0\). $$ f(x)=\sqrt{x-1} $$

Short Answer

Expert verified
The function \(f(x)=\sqrt{x-1}\) is greater than or equal to zero for the interval [1, \(\infty\)).

Step by step solution

01

Graph the Function

The function \(f(x)=\sqrt{x-1}\) can be graphed by taking points along the x-axis and calculating their corresponding y-values by substituting into the function. Remember that we can only take square root of non-negative numbers, so the function is defined for \(x \geq 1\). Calculate a few points for \(x \geq 1\) and plot the points to draw the curve.
02

Interpret the Graph

Looking at the graph, we can notice that: 1) The function is undefined for \(x < 1\). 2) The function is defined and non-negative for \(x \geq 1\), for any value of x greater than or equal to 1, the function is above or on the x-axis i.e., its value is greater than or equal to zero.
03

Write down the Interval

From our interpretation in step 2, we know that the function is greater than or equal to zero for \(x \geq 1\). Therefore, we can write the interval as [1, \(\infty\)).

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