A2-column table with 9 rows. the first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. the second column is labeled f of x with entries 18, 9, 6, 3, 0, negative 3, negative 6, negative 9, negative 18.
based on the table, which best predicts the end behavior of the graph of f(x)

The expression that best predicts the end behavior of the graph of f(x) is the option

As x → ∞, f(x) → -∞, and as x → -∞, f(x) → ∞

The reason why the selected option is correct is given as follows:

Question options; The question options include;

As x → ∞, f(x) → ∞, and as x → -∞, f(x) → ∞

As x → ∞, f(x) → ∞, and as x → -∞, f(x) → -∞

As x → ∞, f(x) → -∞, and as x → -∞, f(x) → ∞

As x → ∞, f(x) → -∞, and as x → -∞, f(x) → -∞

The given data in the table are presented as follows;

From the data, we have;

As x increases to -∞, f(x)  increases to ∞, therefore, we have;

x → -∞, f(x) → ∞

Similarly, we have;

As x → ∞, f(x) → -∞

Therefore, the end behavior of the graph is as x → ∞, f(x) → -∞, and as x → -∞, f(x) → ∞

learn more about the end behaviors of a function here:

link

- 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) ⇒ -∞

f(x)=(x+1)^2-2 is the minimum and g(x)=-(x-2)^2+1 is the maximum

Step-by-step explanation:

Looking at the graph, (you should be able to graph this) the parabola for f(x)=(x+1)^2-2 is pointing downwards and stops at the vertex. This vertex is negative which is the lowest point possible which makes it the minimum. The parabola for -(x-2)^2+1 is pointing upwards and stops at the vertex which is the highest point possible which makes it the maximum.