Find an equation with vertical asymptotes 1 and 4 and horizontal asymptote 1

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).

$450

step-by-step explanation:

first, you have to multiply 150x2=300

next, you have to add 150+300= 450

2 and 1.

step-by-step explanation:

plug in each answer. 0 doesn't work, 1 does. so does 2. 4 doesn't:

0 = 1 is not true.

2 = 2 is true.

4 = 4 is true.

8 = 16 is not true.

hope this !