Answer:
Second option:
- As x decreases without bound, f(x) increases without boud.
- As x increases without bount, f(x) approaches the line y = 0.
Explanation:
The end behavior of a function describes what values may take the function when x increases toward the extremes, i.e. when x approaches +∞ and -∞.
The graph of a function must show the end behavior of a function.
From the attached graph, you can see that as x gets smaller (more negative) the function becomes exponentially larger. In a table that would look like:
x f(x) (approximate value reading the y-coordinate from the graph)
0 1
-1 1.4
-2 2
-3 2.9
-4 4.1
-5 6
And the trend continues, so you can tell by induction that, as x decreases without bound, f(x) increases without bound.
On the other hand, looking at the right side of the graph, you can see that as x increases (gets larger and larger) the function approaches the y-axis, but seems that it never touches it.
That can be formalized if you take the limit of f(x) = (7/10)ˣ, when x approaches + ∞: since the denominator of the fraction (10) is bigger than the numerator (7) as x increases the quotient will become smaller and smaller without reaching 0. For example: (7/10)¹⁰⁰ ≈ 3 × 10⁻¹⁶.