Question

Help!
Attachment#1: I've got no idea how to solve this bad boy.
Attachment#2: Should the domain be (-∞, 1] or [-5, 1]. Ima kinda gettin' confused between the two, please clarify :))

Answer 1

#1

Option (a) is correct

#2

( -∞, 1 ]

Answer 2

Answer 1 :

• Option (a) is the correct option.

There is no doubt that, as the graph is moving rightward ( or towards +ve infinity on x axis ), the value of f(x) ( or y ) is tending towards infinity.

Similarly as the graph is approaching -ve infinity on x axis, the value of f(x) is approaching to -ve infinity.

[ f(x) = y ]

Hence option (a) is absolutely the correct option.

Answer 2 :

• Answer is ( -∞, 1 ]

By noticing the given graph, we can see that the critical point, or the point where the graph is changing its nature from increasing or decreasing is (1,-8) or just 1 unit on x axis.

Before the 1 unit on x axis, the graph is of decreasing nature whereas after the 1 unit on x axis, the graph changed its nature to an increasing one.

We know that domain is the set of all the possible input values ( or the values of x ) in a function.

Therefore, the domain on which the given function is decreasing is ( -∞, 1 ].

Here, ( and ) are used to represent open intervals whereas [ and ] are used for close intervals.