Write the equation of a rational function f(x) = p(×)/q(x) having the indicated properties, in which the degrees of p and q are
as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties.
134.) f has a vertical asymptote given by x=3, a horizontal asymptote y=0, y-intercept at -1, and no x-intercept
135.) f has vertical asymptotes given by x=-2 and x=2, a horizontal asymptote y=2, intercept at 9/2, x-intercepts at -3 and 3, and y-axis symmetry
Please helppp, thank youu
134.) f has a vertical asymptote given by x=3, a horizontal asymptote y=0, y-intercept at -1, and no x-intercept
135.) f has vertical asymptotes given by x=-2 and x=2, a horizontal asymptote y=2, intercept at 9/2, x-intercepts at -3 and 3, and y-axis symmetry
Please helppp, thank youu
1 answer:
Answer:
134. y = 3 / (x-3) attachment picture 1
135. y = (2*(x+3)(x-3)) / (x+2)(x-2) attachment picture 2
Step-by-step explanation:
134. y = 3¹ / (x¹-3)
135. y = (2*(x+3)(x-3)) / (x+2)(x-2)
Apply the asymptote properties to verify, such as compare the degree of numerator and denominator... denominator approach 0 etc.
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Answer:
We know that:
Price of a taco = $4
Price of a burrito = $6.50
x = number of tacos sold
y = number of burritos sold.
We must have that:
x + y ≤ 150 (Because she only has supplies to make 150 tacos or burritos, but she can sell less than that)
And also we know that she must sell at least $780, then:
x*$4 + y*$6.50 ≥ $780
Now we found the system of inequalities:
x + y ≤ 150
x*$4 + y*$6.50 ≥ $780
To solve it graphically, we just need to find each one of the region solutions for each equation, and the intersection of these regions will be the solution for the system.
To graph them may be easier to write them as lines, you can do it as follows:
y ≤ 150 - x
y ≥ ($780 - x*$4)/$6.50
in the first equation, we will shade the area below the line, and in the second equation, we will shade the area above the line.
You can see the image below.
Where the accepted solutions are the ones in the darker part, and we only restrict this to positive values of x (because of how we defined the variable x)
Then looking at the image, we can see that one solution can be the point
x = 20, y = 120
