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Question

# a. Sketch the graph of $f(x)=x^{2}-\frac{3}{x}$, for $-4 \leq x \leq 4$. b. Write down the equation of the vertical asymptote of f(x). c. On the same diagram draw the graph of $g(x)=-3(2)^{x}+9$, for $-4 \leq x \leq 4$. d. Write down the equation of the horizontal asymptote of g(x). e. Find the coordinates of the points of intersection of f(x) and g(x).

Solution

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a. Notice that $f(x)$ is not defined when $x=0$ because division by zero is not defined. So, the graph of $f$ will consist of two branches, one left of $x=0$ ($y$-axis) and one right of $x=0$. Find a few points on the left branch of the graph (when $x<0$). Use table of values.

$x$ $-4$ $-3$ $-2$ $-1$ $-0.5$
$f(x)$ $16.75$ $10$ $5.5$ $4$ $6.25$

Plot the points from the table and draw a smooth curve through them.

Find a few points on the right branch of the graph (when $x>0$). Use table of values.

$x$ $1$ $2$ $3$ $4$
$f(x)$ $-2$ $2.5$ $8$ $15.25$

Plot the points from the table and draw a smooth curve through them.

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