Question

true or false? the piecewise function that is shown in the coordinate plane below is represented by the equation $f(x)=\

$$\begin{cases}5&x\\leq -1\\\\-x + 3&x > -1\\end{cases}$$

$. select the correct answer false true

Explanation:

Step1: Check the first piece ($x \leq -1$)

The first part of the piecewise function is $f(x) = 5$ for $x \leq -1$. Looking at the graph, when $x = -1$, there is a closed dot at $y = 5$, and the horizontal line extends to the left, which matches $f(x) = 5$ for $x \leq -1$.

Step2: Check the second piece ($x > -1$)

The second part is $f(x) = -x + 3$ for $x > -1$. Let's test a point. When $x = 0$, $f(0) = -0 + 3 = 3$. Looking at the graph, when $x = 0$, the point is at $y = 3$, which matches. When $x = 3$, $f(3) = -3 + 3 = 0$, and the graph crosses the x - axis at $x = 3$, which also matches. The slope of $-x + 3$ is $-1$, and the line in the graph for $x > -1$ has a slope of $-1$ (since for every 1 unit increase in $x$, $y$ decreases by 1), and the y - intercept is 3, which matches the equation. Also, at $x=-1$, for the second piece, $f(-1)=-(-1)+3 = 4$, and the graph has an open dot at $x = -1$, $y = 4$, which is consistent with $x > -1$ (the open dot means $x=-1$ is not included in this piece).

Answer:

True