Solution assignment 08 Fractional functions and graphs

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Assignment 8

Given the function:

$y=\displaystyle\frac{x^2-1}{x+1}$

Find:
the vertical asymptote;
the horizontal asymptote;
the intersection point with the $Y$ -as if it exists;
the intersection point with the $X$ -as if it exists.

Based on these results sketch the result in the figure.

Solution

The function looks like a fraction but actually it is not. We can simplify the function:

$y=\displaystyle\frac{x^2-1}{x+1}=\displaystyle\frac{(x+1)(x-1)}{x+1}=x-1$ voor $x\neq{-1}$

Actually the function is a straight line which is not defined for $x=-1$ . However, we can see:

$\displaystyle\lim_{x\to{-1}}(x-1)=-2$

The graph of the original function is actually a straight line with a small 'hole' for $x=-1$ . At the same time we know that the function approaches $y=-2$ if $x$ approaches (either from the left or the right) $-1$ .

Return to Assignments Fractional functions and graphs

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Solution assignment 08 Fractional functions and graphs

Assignment 8

Solution

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