Question

question
the given function $f(x)$ is defined on the interval $-9, 9$ and represented by the graph below. find the $x$-value(s) at which the absolute maximum value of $f(x)$ occurs.
answer attempt 1 out of 2
add value no values

Explanation:

Step1: Understand Absolute Maximum

The absolute maximum of a function on an interval is the highest \( y \)-value the function attains, and we need to find the corresponding \( x \)-value(s).

Step2: Analyze the Graph's Peaks

Look at all the points on the graph (the black dots) and their \( y \)-coordinates.

• The point at \( x = -9 \) has a low \( y \)-value (around -6).
• The point at \( x = -2 \) has a \( y \)-value of 6.
• The point at \( x = 6 \) has a \( y \)-value of 5.
• Other points (like \( x = 1 \) with \( y = -3 \), \( x = 9 \) with \( y = -4 \)) have lower \( y \)-values.

Compare the \( y \)-values: 6 (at \( x = -2 \)) is higher than 5 (at \( x = 6 \)) and the other lower values. So the highest \( y \)-value occurs at \( x = -2 \).

Answer:

\( x = -2 \)