How do you sketch the graph of #1/(x^24)#?
Try different x values to get function's value and then plot it
Plot it accordingly:
graph{1/((x^2)4) [10, 10, 5, 5]}
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To sketch the graph of ( \frac{1}{x^2  4} ), follow these steps:

Identify the vertical asymptotes: Set the denominator equal to zero and solve for ( x ). In this case, ( x^2  4 = 0 ) gives us ( x = 2 ) and ( x = 2 ). These are the vertical asymptotes.

Identify the horizontal asymptote: As ( x ) approaches positive or negative infinity, the function approaches zero. Therefore, the horizontal asymptote is ( y = 0 ).

Find the intercepts: The ( y )intercept occurs when ( x = 0 ), giving ( y = \frac{1}{4} = \frac{1}{4} ). There are no ( x )intercepts.

Determine the behavior between asymptotes: Test points in each interval defined by the vertical asymptotes to determine the behavior of the function.

Sketch the graph: Using the information gathered from the previous steps, plot the asymptotes, intercepts, and the behavior between asymptotes, and then draw the graph accordingly.
The final graph should show the vertical asymptotes at ( x = 2 ) and ( x = 2 ), a horizontal asymptote at ( y = 0 ), and a curve approaching the asymptotes but never touching or crossing them.
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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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