Question

graph the following function on the axes provided.
f(x)=\begin{cases}-6&\text{for }x < 2\\x - 7&\text{for }x>5end{cases}

Explanation:

Step1: Analyze the first - part of the piece - wise function

For $f(x)=-6$ when $x < 2$, this is a horizontal line at $y = - 6$. We draw an open - circle at the point $(2,-6)$ (since $x$ is strictly less than 2) and extend the line to the left.

Step2: Analyze the second - part of the piece - wise function

For $f(x)=x - 7$ when $x>5$. First, find the $y$ - value when $x = 5$. Substitute $x = 5$ into $y=x - 7$, we get $y=5 - 7=-2$. But since $x>5$, we draw an open - circle at the point $(5,-2)$. Then, for other values of $x$ greater than 5, we can find some points. For example, when $x = 6$, $y=6 - 7=-1$. We can plot more points and draw the line $y=x - 7$ for $x>5$.

Answer:

Graph a horizontal line $y = - 6$ with an open - circle at $(2,-6)$ extending to the left and a line $y=x - 7$ with an open - circle at $(5,-2)$ extending to the right.