Question

precalculus unit 2 functions
2.6 notes graphing piecewise functions in pieces
learning target: i can describe and graph each part of a piecewise function and explain how the intervals determine where each piece belongs.
look at the piece of the function your group has been given: f(x)=1 for - 1≤x≤3
what kind of function is your piece?
where does your interval start?
where does it end?
sketch your piece of the graph below?
what questions did you ask yourself while you were graphing?

Explanation:

Step1: Identify function type

The function $f(x) = 1$ for $- 1

Step2: Determine interval start

The interval starts at $x=-1$. Since it is a strict inequality ($-1 < x$), the graph will have an open - circle at $x = - 1$.

Step3: Determine interval end

The interval ends at $x = 3$. Since it is a non - strict inequality ($x\leq3$), the graph will have a closed - circle at $x = 3$.

Step4: Sketch the graph

The graph is a horizontal line at $y = 1$ from $x=-1$ (open - circle) to $x = 3$ (closed - circle).

Answer:

The function is a constant function. The interval starts at $x=-1$ (open - circle) and ends at $x = 3$ (closed - circle). The graph is a horizontal line $y = 1$ between these two points. When graphing, one might ask oneself questions like "Is the point at the start/end included?" and "What is the $y$ - value of the function?".