Answer:
Step-by-step explanation:
Our expression is: .
Let's focus on the cube root of 81 first. What's the prime factorisation of 81? It's simply: 3 * 3 * 3 * 3, or . Put this in for 81:
We know that the cube root of 3 cubed will cancel out to become 3, but the cube root of 3 cannot be further simplified, so we keep that. Our outcome is then:
Now, let's multiply this by 1/3, as shown in the original problem:
Thus, the answer is .
<em>~ an aesthetics lover</em>
Answer:
Domain: (-∞, ∞) or All Real Numbers
Range: (0, ∞)
Asymptote: y = 0
As x ⇒ -∞, f(x) ⇒ 0
As x ⇒ ∞, f(x) ⇒ ∞
Step-by-step explanation:
The domain is talking about the x values, so where is x defined on this graph? That would be from -∞ to ∞, since the graph goes infinitely in both directions.
The range is from 0 to ∞. This where all values of y are defined.
An asymptote is where the graph cannot cross a certain point/invisible line. A y = 0, this is the case because it is infinitely approaching zero, without actually crossing. At first, I thought that x = 2 would also be an asymptote, but it is not, since it is at more of an angle, and if you graphed it further, you could see that it passes through 2.
The last two questions are somewhat easy. It is basically combining the domain and range. However, I like to label the graph the picture attached to help even more.
As x ⇒ -∞, f(x) ⇒ 0
As x ⇒ ∞, f(x) ⇒ ∞
