Math Snap

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function, with two different rules for different ranges of $x$.
. We need to evaluate $f(6)$ and graph the function $f(x)$.

STEP 2

We first need to determine which rule to use when evaluating $f(6)$. To do this, we need to see which range $x =6$ falls into.
The ranges given are $-2 \leq x \leq$ and $< x \leq5$.

STEP 3

We can see that $x =6$ does not fall into either of the given ranges. Therefore, $f(6)$ is undefined.

STEP 4

Now, let's move on to graphing the function $f(x)$. The first part of the function is $2x$ for $-2 \leq x \leq3$. This is a straight line with a slope of2 and it includes the points where $x = -2$ and $x =3$.

STEP 5

The second part of the function is a constant $4$ for $3 < x \leq5$. This is a horizontal line at $y =4$, and it includes the point where $x =5$ but does not include the point where $x =3$ (since $3 < x$).

Putting these two parts together, we can draw the graph of the function $f(x)$.