## Related questions with answers

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

Verified**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.

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Oxford IB Diploma Program: IB Mathematical Studies Standard Level Course Book

2nd Edition•ISBN: 9780198390138Jane Forrest, Jim Fensom, Paula Waldman De Tokman, Peter Blythe#### Physics for the IB Diploma

6th Edition•ISBN: 9781107628199K. A. Tsokos, Mark Headlee, Peter Hoeben#### Milady Standard Cosmetology 2016

1st Edition•ISBN: 9781285769417Milady Standard Cosmetology#### IB Biology Student Workbook

2nd Edition•ISBN: 9781927173930Richard Allan, Tracey Greenwood## More related questions

- integrated math

1/4

- integrated math

1/7