How do you graph #y=7/x+3# using asymptotes, intercepts, end behavior?
horizontal asymptote at
Vertical asymptote at
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To graph the function ( y = \frac{7}{x + 3} ), you can follow these steps:

Vertical Asymptote: Set the denominator equal to zero to find the vertical asymptote. In this case, ( x + 3 = 0 ) gives ( x = 3 ) as the vertical asymptote.

Horizontal Asymptote: As ( x ) approaches positive or negative infinity, the function approaches zero. So, there is a horizontal asymptote at ( y = 0 ).

Intercepts: To find the ( y )intercept, set ( x = 0 ) and solve for ( y ). [ y = \frac{7}{0 + 3} = \frac{7}{3} ] So, the ( y )intercept is ( \left(0, \frac{7}{3}\right) ). There is no ( x )intercept.

End Behavior: As ( x ) approaches positive infinity, ( y ) approaches zero. As ( x ) approaches negative infinity, ( y ) also approaches zero.

Plotting:
 Plot the vertical asymptote at ( x = 3 ).
 Plot the horizontal asymptote at ( y = 0 ).
 Plot the ( y )intercept at ( \left(0, \frac{7}{3}\right) ).
 As ( x ) approaches ( 3 ) from the left, ( y ) approaches negative infinity, and as ( x ) approaches ( 3 ) from the right, ( y ) approaches positive infinity.
 Draw the curve approaching the asymptotes, avoiding crossing them.
By following these steps, you can graph the function ( y = \frac{7}{x + 3} ) accurately, showing its asymptotes, intercepts, and 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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