Question

y = f(x)
○ linear○ quadratic○ neither
type lowercase o twice for ∞. if no interval exists type dne.
increasing:
decreasing:
constant:
domain:
range:
question help: message instructor

Explanation:

Step1: Classify function type

A linear function has a constant slope (straight line, no breaks), a quadratic function is a parabola. This piecewise graph has multiple segments with different slopes and breaks, so it is neither.

Step2: Find increasing interval

Identify where the graph rises left to right: from $x=3$ to $+\infty$.

Step3: Find decreasing interval

Identify where the graph falls left to right: from $x=2$ to $x=3$.

Step4: Find constant interval

Identify where the graph is flat: from $x=-5$ to $x=2$.

Step5: Determine domain

The graph starts at $x=-5$ (closed dot) and extends to $+\infty$.

Step6: Determine range

The lowest $y$-value is $0$, highest is $3$, and all values between are covered.

Answer:

○ Linear ○ Quadratic ● Neither
Increasing: $(3, oo)$
Decreasing: $(2, 3)$
Constant: $(-5, 2)$
Domain: $(-5, oo)$
Range: $(0, 3)$