Question

translated up 4 units

1. the graph below shows a function.

which of the following best describes the
range of this function?
a. all real numbers
b. all real numbers between -4 and 0
c. all real numbers less than or equal to -4
d. all real numbers greater than or equal to -4

Explanation:

Step1: Recall Range Definition

Range is the set of all possible \( y \)-values of a function.

Step2: Analyze the Graph

The graph is a parabola opening upwards (since it has a minimum point). The vertex (minimum point) has a \( y \)-coordinate of \(-4\). For an upward - opening parabola, the \( y \)-values start at the minimum \( y \)-value and go to positive infinity. So the range includes all real numbers greater than or equal to \(-4\).

Step3: Evaluate Options

• Option A: All real numbers is incorrect because the parabola has a minimum \( y \)-value, so it doesn't take all real numbers.
• Option B: The graph is not restricted between \(-4\) and \(0\) (it goes above \(0\) as \(x\) moves away from the vertex).
• Option C: The parabola opens upwards, so it doesn't have a maximum at \(-4\), it has a minimum.
• Option D: Matches the analysis of the range (all real numbers \(\geq - 4\)).

Answer:

D. All real numbers greater than or equal to -4