Find an equation with vertical asymptotes 1 and 4 and horizontal asymptote 1 please help
1 answer:
Answer:
y = 1 + 1/((x -1)(x -4))
Step-by-step explanation:
To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.
To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.
Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.
... y = 1 + 1/((x -1)(x -4))
If you like, this can be "simplified" to ...
... y = (x² -5x +5)/(x² -5x +4)
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In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).
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Answer:
The image points are given as;
I' ( -3,0 )
J'( 0,3 )
K'( 2,2)
L'(1,-1 )
Step-by-step explanation:
The object points has coordinates at;
I (5,0)
J(2,3)
K(0,2)
L(1,-1 )
The object points are reflected across line x= 1 to get image of objects points at ;
I' ( -3,0 )
J'( 0,3 )
K'( 2,2)
L'(1,-1 )
Attached is the graph for the object points and image points after reflection across x= 1
