Question

unit test
unit test complete
21 22
the graph of the piecewise function f(x) is shown. what is the range of f(x)?
options:
{ f(x) | -∞ < f(x) < ∞ }
{ f(x) | -∞ < f(x) ≤ 4 }
{ f(x) | 4 < f(x) < ∞ }
{ f(x) | 0 ≤ f(x) < ∞ }
mark this and return save and exit next

Explanation:

Step1: Analyze left segment

The left horizontal segment (x ≤ 0) has f(x) = 4.

Step2: Analyze right segment

The right line (x ≥ 0) starts at (0,4) and decreases to (5,1), so f(x) ranges from 1 up to 4 here.

Step3: Combine ranges

All possible f(x) values are ≤4 (from both segments) with no lower bound shown (the left segment extends infinitely left at y=4, and the right line doesn’t go below 1 but the left keeps y=4; overall max is 4, no min restriction beyond being real numbers ≤4). Thus range is $-\infty < f(x) \leq 4$.

Answer:

B. $\{ f(x) \mid -\infty < f(x) \leq 4 \}$