Question - Analysis of a Function Using Its Graph

Solution:

The domain of \( f \): All real numbers \( x \) such that \( -4 \leq x \leq 5 \).

The range of \( f \): All real numbers \( y \) such that \( -3 \leq y \leq 5 \).

The zeros of \( f \): \( x = -2, 1 \).

\( f(-3.5) \): Cannot be determined exactly from the graph; not provided.

The intervals on which \( f \) is increasing: \( (-4, -3) \cup (1, 5) \).

The intervals on which \( f \) is decreasing: \( (-3, 1) \).

The values for which \( f(x) < 0 \): \( x \) in intervals \( (-2, 1) \).

Any relative maxima or minima: Relative maximum at \( x = -3 \), relative minimum at \( x = 1 \).

The value(s) of \( x \) for which \( f(x) = 3 \): Approximately \( x = 4.5 \).

Is \( f(0) \) positive or negative? Negative, since \( f(0) \) is below the \( x \)-axis.

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