Question

evaluate functions from a graph
score: 12/30 penalty: 1 off
question
find the value of f(8).
y = f(x)
(graph of a piecewise function with axes labeled x and y, x from -10 to 10, y from -10 to 10)
answer attempt 1 out of 5

Explanation:

Step1: Understand the task

To find \( f(8) \), we need to determine the \( y \)-value of the function \( y = f(x) \) when \( x = 8 \) from the graph.

Step2: Locate \( x = 8 \) on the x - axis

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

Step3: Determine the corresponding \( y \)-value

From the graph, when we move up from \( x = 8 \) on the x - axis, we intersect the line part of the graph. By looking at the slope and the equation of the line (or by directly reading the graph), we can see that the line has a slope. Let's assume the line passes through points like \( (4,0) \) and \( (0, - 4) \), the slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0-(-4)}{4 - 0}=\frac{4}{4} = 1 \). The equation of the line (for \( x\geq - 2 \) maybe) is \( y-0=1\times(x - 4) \), so \( y=x - 4 \). When \( x = 8 \), \( y=8 - 4=4 \). Alternatively, by directly looking at the graph, at \( x = 8 \), the \( y \)-coordinate of the point on the graph is 4.

Answer:

\( 4 \)