Question

What is the end behavior of the function f of x equals 3 times the cube root of x? as x → –[infinity], f(x) → –[infinity], and as x → [infinity], f(x) → [infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0.

Answer 1

The function $f(x)=4\sqrt[3]{x}$ is a cube root function and the function end behavior is: $x$ → $+$ ∞, $f(x)$ → $+$ ∞, and as $x$ → - ∞, $f(x)$ → $+$ ∞

What is end behavior?

• The end behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis.
• In other words, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ).

To determine the end behavior:

• The equation of the function is given as: $f(x)=4\sqrt[3]{x}$
• To determine the end behavior, we plot the graph of the function f(x).
• We can see from the accompanying graph of the function:
• As x approaches infinity, so does the function f(x), and vice versa.
• As a result, the function end behavior is:  

$x$ → $+$ ∞, $f(x)$ → $+$ ∞, and as $x$ → - ∞, $f(x)$ → $+$ ∞

Therefore, the function $f(x)=4\sqrt[3]{x}$ is a cube root function and the function end behavior is: $x$ → $+$ ∞, $f(x)$ → $+$ ∞, and as $x$ → - ∞, $f(x)$ → $+$ ∞

Know more about functions' end behavior here:

brainly.com/question/1365136

#SPJ4

The complete question is given below:

What is the end behavior of the function f of x equals negative 4 times the cube root of x?

As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.

As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.

As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.

As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.