Question

identify each characteristic for the graph of the function shown. decide whether the function has extrema: add extremum no extrema select a statement that describes the function: describe the end behavior: as x → -∞, y → as x → ∞, y →

Explanation:

Step1: Check for Extrema

A function has extrema (local maxima or minima) if there are points where the graph changes direction (from increasing to decreasing or vice versa). The given graph has a low point (local minimum) and a high point (local maximum), so it has extrema. Thus, we choose "Add extremum".

Step2: Analyze End Behavior (As \( x \to -\infty \))

For the left - hand end (as \( x \) approaches \( -\infty \)), we look at the direction of the graph. The graph goes up (towards positive infinity) as \( x \) becomes very negative. So as \( x \to -\infty \), \( y \to \infty \) (or \( +\infty \)).

Step3: Analyze End Behavior (As \( x \to \infty \))

For the right - hand end (as \( x \) approaches \( +\infty \)), the graph goes up (towards positive infinity) as \( x \) becomes very large. So as \( x \to \infty \), \( y \to \infty \) (or \( +\infty \)).

Answer:

• Decide whether the function has extrema: Add extremum
• As \( x \to -\infty \), \( y \to \infty \) (or \( +\infty \))
• As \( x \to \infty \), \( y \to \infty \) (or \( +\infty \))