Question

1. Find the horizontal asymptote of the graph of -6x^3+5x+8/x^3+x+8

2. Simplify the rational expression. State any restrictions on the variable. p^2-4p-32/p+4

3. Simplify the rational expression. State any restrictions on the variable. q^2+11q+24/q^2-5q-24

4. Write an equation for the translation of y=-1/x that has the asymptotes x = –2 and y = 4.

Answer 1

the horizontal asymptote if easy find using polynomial division

so basically it occurs at y = -6 because the numerator and denominator are of the same degree.

so its really \[y = \frac{-6x^3}{x^3} = -6\]

if you did the division properly there would be a remainder, which is ignored.

hope this helps

Answer 2

question 2

the restrictions occur in the denominator... it can't be zero so to find the restriction solve

p + 4 = 0

the answer is the restriction.

so simplify the expression factorise the numerator and you'll see a binomial factor will cancel leaving a linear expression. The restriction would become a point of discontinuity rather than a asymptote

Answer 3

Question 3 similar to question 2

factorise the numerator and denominator

factors will cancel. the restrictions will be the values that make the denominator zero, easy to find after factoring.

Answer 4

question 4 to get a horizontal asymptote of y =4

the numerator would need to be 4x

the vertical is found by expression the asymptote

x = -2 in terms of x + 2 = 0

x + 2 becomes the new denominator.

Answer 5

@campbell_st so number 2 is \[p+8;p \neq 4\]

Answer 6

?

Answer 7

nope the denominator is

p + 4

so solve

p + 4 = 0

that is the restriction

and factor

\[x^2 - 4x - 32\]

find the factors of -32 that add to -4, the larger factor is negative.

Answer 8

thank you so much