Questions: Sketch a graph of f(x) = 1 if x ≤ -2, -x - 1 if -2 < x ≤ 1, -1 if x > 1.

Solution Steps

For $x \le -2$, the function is $f(x) = 1$. This is a horizontal line at $y=1$. Since $x$ is less than or equal to $-2$, we use a closed circle at the point $(-2, 1)$ and draw the horizontal line to the left.

For $-2 < x \le 1$, the function is $f(x) = -x - 1$. This is a line with a slope of $-1$ and a $y$-intercept of $-1$. Since $x$ is greater than $-2$ but less than or equal to $1$, plot an open circle at $x = -2$ and find $f(-2) = -(-2) - 1 = 2 - 1 = 1$, so $(-2, 1)$ has an open circle. At $x=1$, $f(1) = -1-1 = -2$, so we put a closed circle at $(1, -2)$. Draw a segment connecting these two points.

For $x > 1$, the function is $f(x) = -1$. This is a horizontal line at $y=-1$. Since $x$ is greater than $1$, use an open circle at the point $(1, -1)$ and draw the line to the right.

Final Answer: