Question

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question
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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 until we intersect the graph of \( y = f(x) \).

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

Looking at the graph, when \( x = 6 \), the peak of the graph (the vertex of the piece - wise function) is at \( y = 8 \). Then, as \( x \) increases from 6 to 8, the graph is a line decreasing from \( (6,8) \) to \( (8,4) \) (we can check the slope or just the pattern). The slope between \( (6,8) \) and \( (8,4) \) is \( \frac{4 - 8}{8 - 6}=\frac{- 4}{2}=-2 \). Using the point - slope form \( y - y_1=m(x - x_1) \) with \( (x_1,y_1)=(6,8) \) and \( m=-2 \), when \( x = 7 \), \( y-8=-2(7 - 6) \), \( y-8=-2(1) \), \( y=8 - 2 = 6 \). Alternatively, by visually inspecting the graph, at \( x = 7 \), the \( y \)-coordinate of the point on the graph is 6.

Answer:

6