Question

question
find the value of f(2).
y = f(x)
answer attempt 1 out of 2

Explanation:

Step1: Understand \( f(2) \) meaning

\( f(2) \) is the \( y \)-value when \( x = 2 \) on the graph \( y = f(x) \).

Step2: Locate \( x = 2 \) on x - axis

Find \( x = 2 \) on the horizontal (x) axis. Then, move vertically to intersect the graph of \( y = f(x) \).

Step3: Determine the \( y \)-value

From the graph, at \( x = 2 \), the corresponding \( y \)-value (by moving up/down from \( x = 2 \) to the graph) is 7. Wait, let's re - check. Wait, the left - hand line: let's find the equation of the left - hand line. The left - hand line passes through \( (-5,0) \) and \( (0,5) \). The slope \( m=\frac{5 - 0}{0-(-5)}=\frac{5}{5}=1 \). So the equation is \( y-0 = 1\times(x + 5) \), i.e., \( y=x + 5 \). When \( x = 2 \), \( y=2 + 5=7 \). Wait, but wait, the peak is at \( x = 4 \) (since at \( x = 4 \), \( y = 9 \)). So for \( x \) from \( - 5 \) to \( 4 \), the function is \( y=x + 5 \). So at \( x = 2 \), \( y=2 + 5 = 7 \). Wait, but let's check the graph again. The grid: each square is 1 unit. At \( x = 0 \), \( y = 5 \); at \( x = 1 \), \( y=6 \); at \( x = 2 \), \( y = 7 \); at \( x = 3 \), \( y = 8 \); at \( x = 4 \), \( y = 9 \). Yes, so when \( x = 2 \), \( y=7 \).

Answer:

7