Question

find the value of $f(-5)$.
$y = f(x)$
(there is a graph of a piece - wise linear function $y = f(x)$ with a coordinate grid. the x - axis ranges from - 10 to 10 and the y - axis ranges from - 10 to 10. the graph has two line segments. one segment goes from the left (upwards) and intersects the x - axis at $x=-2$, and the other goes from the vertex (around $x = 2,y=-3$) upwards and intersects the x - axis at $x = 4$.)
answer attempt 1 out of 2
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Explanation:

Step1: Locate x = -5 on the graph

To find \( f(-5) \), we first find the point on the x - axis where \( x=-5 \). Then we look at the corresponding point on the graph of \( y = f(x) \) to determine the y - value (since \( f(x)=y \)).

Looking at the graph of the piece - wise function, the left - hand line (the line with a negative slope) passes through points. We can also use the fact that for the left - hand segment of the function (the line going from the left towards the vertex), we can determine the y - value when \( x=-5 \).

We can see from the grid of the graph that when \( x = - 5\), we move up from \( x=-5 \) until we hit the graph of \( y = f(x) \). By looking at the y - coordinate of the point on the graph where \( x=-5 \), we observe that the y - value is 4.

Answer:

4