Answer:
- When the values of x ⇒ -∞, f(x) ⇒ +∞
- When the values of x ⇒ +∞, f(x) ⇒ -∞
Step-by-step explanation:
* Lets explain the end behavior of the graph of a function
- The end behavior of a function f describes the trend of the graph
if we look to the right end of the x-axis as x approaches ∞ and
to the left end of the x-axis as x approaches -∞
- Lets look to the table of the function
x f(x)
-4 18
-3 9
-2 6
-1 3
0 0
1 -3
2 -6
3 -9
4 -18
* From the table we notice that
- The values of x from -4 to zero have positive values of f(x)
- The values of x from 0 to 4 have negative values of f(x)
∴ When x increased from negative to positive y decreased from
positive to negative
- That means when x values go to -∞ the corresponding values of
f(x) go to +∞ and when x values go to +∞ the corresponding values of
f(x) go to -∞
∴ The end behavior of the graph of f(x) is
- When the values of x ⇒ -∞, f(x) ⇒ +∞
- When the values of x ⇒ +∞, f(x) ⇒ -∞
