Question

evaluate functions from a graph
score: 28/30 penalty: 1 off
question
find the value of f(7).
y = f(x)
answer attempt 2 out of 2

Explanation:

Step1: Understand the problem

We need to find \( f(7) \) from the graph of \( y = f(x) \). This means we look for the \( y \)-value when \( x = 7 \) on the graph.

Step2: Locate \( x = 7 \) on the x - axis

Find the point on the x - axis where \( x = 7 \). 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/down from \( x = 7 \) to the graph, we can see the slope of the line for \( x\geq4 \) (since the line crosses the x - axis at \( x = 4 \)). Let's find the equation of the line for \( x\geq4 \). We know two points on this line: when \( x = 4 \), \( y = 0 \), and let's take another point, say when \( x = 0 \), \( y = 4 \)? Wait, no, looking at the graph, the line for \( x\geq4 \) has a slope. Let's calculate the slope \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \( (4,0) \) and \( (0,4) \)? No, wait, when \( x = 0 \), \( y = 4 \), but the line for \( x\geq4 \) is a straight line. Wait, actually, when \( x = 4 \), \( y = 0 \); when \( x = 5 \), \( y=- 1 \); \( x = 6 \), \( y=-2 \); \( x = 7 \), \( y=-3 \). So by observing the pattern, for each increase of 1 in \( x \) (starting from \( x = 4 \)), \( y \) decreases by 1. So when \( x = 7 \), which is \( 7-4 = 3 \) units to the right of \( x = 4 \), \( y=0-3=-3 \).

Answer:

\(-3\)