Question

question
find the value of f(9).
y = f(x)
answer attempt 1 out of 2

Explanation:

Step1: Understand the problem

We need to find \( f(9) \) from the graph of \( y = f(x) \). This means we look for the \( y \)-value when \( x = 9 \) on the graph.

Step2: Locate \( x = 9 \) on the x-axis

Find the point on the x-axis where \( x = 9 \). Then, find the corresponding point on the graph of \( f(x) \) and determine its \( y \)-coordinate.

Looking at the graph, the line for \( x \geq -2 \) (the right - hand part of the graph) has a slope. Let's analyze the equation of the line for \( x \geq -2 \). We can see that the line passes through \( (2,0) \) and \( (0,2) \)? Wait, no, let's check the slope. Wait, when \( x = 2 \), \( y = 0 \); when \( x = 0 \), \( y = 2 \)? Wait, no, actually, looking at the graph, the right - hand line (the decreasing line) passes through \( (2,0) \) and let's take another point. Let's find the slope \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the right - hand line: say \( (2,0) \) and \( (0,2) \)? Wait, no, when \( x = 0 \), \( y = 2 \); when \( x = 2 \), \( y = 0 \). So the slope \( m=\frac{0 - 2}{2 - 0}=\frac{- 2}{2}=- 1 \). So the equation of the line is \( y-0=-1(x - 2) \), which simplifies to \( y=-x + 2 \).

Now, substitute \( x = 9 \) into the equation \( y=-x + 2 \).

Step3: Calculate \( f(9) \)

Substitute \( x = 9 \) into \( y=-x + 2 \):
\( y=-9 + 2=-7 \)

Alternatively, by looking at the graph, when we move to \( x = 9 \) on the x - axis and then find the corresponding \( y \)-value on the graph of \( f(x) \), we can see that the \( y \)-value is \( - 7 \).

Answer:

\( f(9)=-7 \)