What is the end behavior of f(x)=4x^4-3x^2?
1 answer:
Answer:
as x→∞, y→∞
as x→-∞, y→∞
Step-by-step explanation:
To tell what the end-behavior is, look at the x with highest exponent value in the function.
f(x) = 4x⁴ - 3x²
The highest power is x⁴.
Our highest exponent value is 4.
If the highest power is an even number, the end behavior is:
as x→∞, y→∞
as x→-∞, y→∞
this is always true. It's part of the rule for end-behavior.
The end behavior graph for an even power will look like the graph for x².
This is also always true. It will always look like this if the highest power is an even number.
You might be interested in
Answer:
Increasing on it's domain because the slope is positive.
The domain and range are both all real numbers, also known as
.
Step-by-step explanation:
All domain really means is what numbers can you plug in and you get number back from your function.
I should be able to plug in any number into 3x+2 and result in a number. There are no restrictions for x on 3x+2.
The domain is all real numbers.
In interval notation that is .
Now the range is the set of numbers that get hit by y=3x+2.
Well y=3x+2 is a linear function that is increasing. I know it is increasing because the slope is positive 3. I wrote out the positive part because that is the item you focus on in a linear equation to determine if is increasing or decreasing.
If slope is positive, then the line is increasing.
If slope is negative, then the line is decreasing.
So y=3x+2 hits all values of y because it is increasing forever. The range is all real numbers. In interval notation that is .