Chapter 2.5, Problem 63AYU

To determine

To draw:

The graph of the function at the equation

Explanation of Solution

Given:

The function is   $f\left(x\right)=-{\left(x+1\right)}^2-1$

Concept used:

An equation of a line $l$ through a point $P_1\left(x_1,y_1\right)$ with slope $m$ . If $P\left(x,y\right)$ is any point with $x\ne x_1$

Then P is on $l$ if and only if the slope of the line through $P_1$ and P

The equation is $y-y_1=m\left(x-x_1\right)$

Calculation:

The function

  $f\left(x\right)=-{\left(x+1\right)}^2-\mathrm{1...................}\left(1\right)$

Draw the table   $y=f\left(x\right)=-{\left(x+1\right)}^2-1$

Test one point in each of the region formed by the graph

If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function

$x-axis$	$-1$	$0$	$-2$	$0.44$
$y-axis$	$-1$	$-2$	$-2$	$-3$