How do you graph #f(x)=x^44# using zeros and end behavior?
Find the zeros, end behavior and y intercept as described below.
Graph
To find the zeros, factor the polynomial.
Factor again.
Setting each factor equal to zero and solving gives:
The only real zeros are
To find the end behavior, examine the degree and leading coefficient of the original polynomial.
The degree is
An even degree with a positive leading coefficient indicates that as
It is also helpful to find the
The graph is shown below.
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To graph the function f(x) = x^4  4 using zeros and end behavior, follow these steps:

Find the zeros of the function by setting f(x) equal to zero and solving for x. x^4  4 = 0 x^4 = 4 x = ±√2 and x = ±√(2) (since x^4 = (x)^4) The real zeros are x = √2 and x = √2.

Determine the end behavior of the function as x approaches positive and negative infinity. Since the leading term of the polynomial is x^4, the end behavior is the same as that of a fourthdegree polynomial, which means:
 As x approaches positive infinity, f(x) approaches positive infinity.
 As x approaches negative infinity, f(x) approaches positive infinity.

Plot the zeros (√2, 0) and (√2, 0) on the graph.

Sketch the graph of the function approaching positive and negative infinity based on the end behavior determined in step 2.
Combining these steps, you can sketch the graph of f(x) = x^4  4 using the zeros (√2, 0) and (√2, 0) and considering its end behavior.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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