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Calculus, 8th Edition,stewart; page 19 problem 9

Determine whether the curve is the graph of a function of x. if it is, state the domain and range of the function.

asked Jul 27, 2015 in CALCULUS by anonymous

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1 Answer

Step:1

Vertical Line Test :

A curve in the $xy-$ plane is the graph of a function of $x$ if and only if no vertical line intersects the curve more than once.

Observe the graph.

Draw a vertical line along the $y-$ axis, the line touches the curve only once.

The graph of the function passes the vertical line test.

Hence, by the definition of vertical line test, the graph is a function of $x$ .

Step:2

The domain is the set of all values of $x$ on the curve.

The curve is defined for $-3\leqslant x\leqslant 2$ .

The domain of the function is $\left [ -3, 2 \right ]$ .

The range is the set of all values of $y$ on the curve.

The curve takes all the value from $-3$ to $-2$ (except $-2$ ) and $-1$ to $3$ .

The range of the function is $(-3, -2)\cup \left [ -1, 3 \right ]$ .

Solution:

Yes, graph is a function of $x$ .

The Domain and range of the curve is $\left [ -3, 2 \right ]$ and $(-3, -2)\cup \left [ -1, 3 \right ]$ .

answered Jul 27, 2015 by dozey Mentor

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