Use the provided information to sketch the graph of $f$ . Assume that $f$ is continuous on its domain and that all intercepts are included in the table of values.

Domain: All real $x$ , except $x=-1;$
$f(-3)=2,f(-2)=3,f(0)=-1,f(1)=0;$ $f'(x)>0\ \text{on}\ (-\infty,-1)\ \text{and}\ (-1,\infty)$ $f''(x)>0\ \text{on}\ (-\infty,-1); f''(x)<0\ \text{on}\ (-1,\infty);$
vertical asymptote: $x=-1;$

horizontal asymptote: $y=1$

Question

Use the provided information to sketch the graph of $f$. Assume that $f$ is continuous on its domain and that all intercepts are included in the table of values.

Domain: All real $x$, except $x=-1;$

$$
f(-3)=2,f(-2)=3,f(0)=-1,f(1)=0;
$$

$$
f'(x)>0\ 	ext{on}\ (-\infty,-1)\ 	ext{and}\ (-1,\infty)
$$

$$
f''(x)>0\ 	ext{on}\ (-\infty,-1); f''(x)<0\ 	ext{on}\ (-1,\infty);
$$

vertical asymptote: $x=-1;$

horizontal asymptote: $y=1$

Quizlet Admin · Accepted Answer

To sketch the graph of $f$, we need to determine the intervals where it is increasing, decreasing, concave upward, concave downward, and the asymptotes.

Note that if $f'(x)$ is positive then $f(x)$ is increasing, and if $f'(x)$ is negative then $f(x)$ is decreasing.

$f'(x)$ is positive on $(-\infty,-1)$.
So, $f(x)$ is increasing on $(-\infty,-2)$.

$f'(x)$ is positive on $(-1,\infty)$.
so, $f(x)$ is increasing on $(-1,\infty)$.

Create an account to view solutions

Create an account to view solutions

Related questions