Notice from the graph that there is no jump, vertical asymptotes, or hole in the graph of the function. Hence, it implies that the function is continuous over the entire domain.
From the graph, the function is decreasing over its entire domain. It, therefore, follows that there is no interval the function is increasing.
Respond with an empty set for the increase interval.
Since the function decreases over its entire domain, (-∞,∞), it follows that the decrease interval is (-∞,∞).
Notice from the graph that the function has no maximum value since the function tends to +∞ as x decreases.
Respond with an empty set for the maximum.
Notice from the graph that the function just approaches y=3 but does not touch it. Hence, there is a horizontal asymptote at y=3. This implies that the function does not have a minimum value as it keeps on decreasing while it approaches 3 but will never equal 3.
Respond with an empty set for the minimum.
To find f(x) when x=-3, substitute x=-3 into the function and evaluate:
Hence, f(x)=35 when x=-3.
To find f(x) when x=17, substitute x=17 into the function and evaluate:
Hence, f(x)=98305/32768 when x=17.
From the graph, notice that as x goes small, i.e. as it tends towards negative infinity (the left), the function tends to positive infinity.
Hence, as x→-∞, f(x)→+∞.
Since the graph approaches y=3 as x tends to positive infinity (the right), it follows that as x→+∞, f(x)→3.
The function does not have a vertical asymptote, so respond with an empty set.
The function has a horizontal asymptote, y=3.