Question 181650
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You can run a calculator as well as I can, so just punch in the values you have for <i>x</i>, hit the "Sqrt" button, and write down the results in the *[tex \Large sqrt{x}] column.

Once you have filled out your table, each of the rows represents a pair of coordinates, (<i>x</i>,<i>y</i>) = (<i>x</i>, *[tex \Large sqrt{x}] ).  Plot these points on your graph and draw a smooth curve through the points.

As to the question, "Is the graph a function?"  Technically, no.  Any graph is merely a picture of a mathematical relationship and that relation may or may not be a function. Therefore the graph itself cannot be a function or anything other than a graph for that matter.  The appropriate question would be "Is the relation illustrated by the graph a function?"

The definition of a function requires that the value of the function be unique for any given value of the independent variable.  This means that if something is a function in <i>x</i>, then there is no possible value of <i>x</i> that would return more than one value.  Graphically, you can answer the question using the Vertical Line Test.  Is there any possible vertical line that would intersect the graph of the relation in more than one point?  If the answer is yes, then the relation is <i><b>not</b></i> a function.  Otherwise, it is a function.

The domain of a function is that set of values for the independent variable for which the function is defined.  We know that the square root is undefined on the real numbers for any value of the radicand less than zero, so the domain is all real numbers greater than or equal to 0.  In set builder notation:

Domain: *[tex \Large \{x\ |\ x\ \in\ \R, x \geq 0\}]

The range is that set of values that the function can assume for all values of the independent variable in the domain.  We know that the smallest value for <i>x</i> is zero, and that the square root of <i>x</i> gets larger as <i>x</i> gets larger, so the range is, like the domain, all real numbers greater than or equal to zero.

Range: *[tex \Large \{y\ |\ y\ \in\ \R, y \geq 0\}]

John
*[tex \LARGE e^{i\pi} + 1 = 0]
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