Question

score: 27/30 penalty: 1 off
question
find the value of f(-8).
y = f(x)
(graph of y = f(x) with x-axis from -10 to 10 and y-axis from -10 to 10, showing a piecewise linear function)
answer attempt 1 out of 2

Explanation:

Step1: Understand the graph

The graph of \( y = f(x) \) is given. To find \( f(-8) \), we need to find the \( y \)-value when \( x = -8 \) on the graph.

Step2: Locate \( x = -8 \)

Find the point on the \( x \)-axis where \( x = -8 \). Then, move vertically until we intersect the graph of \( f(x) \).

Step3: Determine the \( y \)-value

From the graph, when \( x = -8 \), the corresponding \( y \)-value (which is \( f(-8) \)) can be found by looking at the line. The left - hand line of the graph (the increasing part) passes through points. We can also use the slope - intercept form of the line. First, find the equation of the left - hand line. We know two points on the left - hand line: for example, when \( x=-3\), \( y = 0 \) and when \( x = 0\), \( y=3\). The slope \( m=\frac{3 - 0}{0-(-3)}=\frac{3}{3} = 1\). The equation of the line using point - slope form \( y - y_1=m(x - x_1)\) with \((x_1,y_1)=(-3,0)\) is \( y-0 = 1\times(x + 3)\), so \( y=x + 3\). Now, substitute \( x=-8\) into the equation: \( y=-8 + 3=-5\). Alternatively, by directly looking at the graph, when \( x=-8\), the \( y\) - coordinate is \(-5\).

Answer:

\(-5\)