Chapter Review
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Start by finding the asymptotes.
Graph:
Domain: All real numbers except 4
Range: All real numbers except 3
To graph the given rational function, we will start by identifying the values of a, b, c, and d. f(x)=3x-2/x-4 ⇔ f(x)=3x+( -2)/1x+(-4) We see above that a = 3, b = -2, c = 1, and d = - 4. With this information, we will find the asymptotes, graph the function, and state the domain and range.
Let's make a table of values to find points on the curve. Make sure to include values of x that are on both sides of the vertical asymptote.
| x | 3x-2/x-4 | f(x)=3x-2/x-4 |
|---|---|---|
| 0 | 3( 0)-2/0-4 | 0.5 |
| 2 | 3( 2)-2/2-4 | -2 |
| 3 | 3( 3)-2/3-4 | -7 |
| 5 | 3( 5)-2/5-4 | 13 |
| 6 | 3( 6)-2/6-4 | 8 |
| 8 | 3( 8)-2/8-4 | 5.5 |
Let's plot and connect the obtained points. Keep in mind that rational functions have two branches. Do not forget to graph the asymptotes!
To state the domain and range of the function, we will consider our graph.
We see that the x-variable takes any value except 4. The y-variable takes any value except 3. Domain:& All real numbers except4 Range:& All real numbers except 3