Question

from the graph of the function, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant. complete parts (a) and (b)
the range is $(-infty, infty)$.
( type your answer in interval notation )
on what interval(s) is the function increasing? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the function is increasing on \boxed{}.
( type your answer in interval notation. use a comma to separate answers as needed )
b. the function is never increasing.
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Explanation:

Step1: Analyze Graph (a)

The graph (a) is a straight line with a negative slope. A negative - slope line means that as \(x\) increases, \(y\) decreases. So, the function in graph (a) is decreasing everywhere.

Step2: Analyze Graph (b)

The graph (b) is a parabola - like curve (a quadratic - type curve opening upwards). For a function to be increasing, as \(x\) increases, \(y\) should increase. The vertex of the parabola (the minimum point) is at some \(x\) - value. To the right of the vertex, as \(x\) increases, \(y\) increases. But wait, let's re - examine the first graph (a). Wait, the question has two graphs? Wait, no, the first part (the top graph) is a line with negative slope. Let's focus on the first function (the top graph). The slope of the line: if we take two points, say, when \(x = 0\), \(y=0\) (assuming the intercept) and another point, as \(x\) increases, \(y\) decreases. So the function is decreasing on \((-\infty,\infty)\) and never increasing. For the second graph (b), but the question's first part (the one with the range \((-\infty,\infty)\))? Wait, no, the user's question: Wait, the first function (top graph) is a line with negative slope. So when we check the interval where it's increasing: since the slope is negative, \(y\) decreases as \(x\) increases. So the function is never increasing.

Answer:

B. The function is never increasing.