Determine the slope from the given graph below:
1 answer:
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<h3>Answer: Choice A</h3>
Why? Because the denominators are both the same at 2x+8. We can only add or subtract fractions when the denominators are the same. The general rule for adding fractions is
We have numerators A and B added together over a common denominator C. If we didn't have a common denominator, then we'd have to do a bit of algebraic manipulation to get both fractions to a common denominator. It doesn't have to be the lowest common denominator (LCD), though it's often more efficient that way.
Check out the attached image below. Use polynomial long division (see figure 1) or synthetic division (figure 2) to find that the quotient is x-8
This tells us the slant asymptote is y = x-8
The presence of the slant asymptote means we do not have a horizontal asymptote. As x gets larger and larger, and heads to infinity, then y approaches the line y = x-8; rather than y approaching some single fixed value.
The vertical asymptote is x = -4 because this x value makes the denominator x+4 equal to 0. We cannot divide by zero.
Figure 3 shows the graph, which I have done using GeoGebra (a free graphing tool). This is also attached below.
