Lets say we have
P(x)/q(x)
vertical assymtotes are in the form x=something, not y=0
y=0 are horizontal assemtotes
so verticall assymtotes
reduce the fraction
set the denomenator equal to zero
those values that make the deomenator zero are the vertical assymtotes
the horizontal assymtote
when the degree of P(x)<q(x), then HA=0
when the degree of P(x)=q(x), then divide the leading coefient of P(x) by the leading coeficnet of q(x)
example, f(x)=(2x^2-3x+3)/(9x^2-93x+993), then HA is 2/9
ok so for vertical assymtote example
f(x)=x/(x^2+5x+6)
the VA's are at x=-3 and x=-2
horizontal assymtote
make degree same
f(x)=(3x^2-4)/(8x^2+9x),
the HA is 3/8
hope I helped, read the whole thing then ask eusiton
Many when you solve it it works out perfectly.
Answer:
Step-by-step explanation:
Isolate the term of n from one side of the equation.
<h3>n-1/8=3/8</h3>
<u>First, add by 1/8 from both sides.</u>
n-1/8+1/8=3/8+1/8
<u>Solve.</u>
<u>Add the numbers from left to right.</u>
3/8+1/8=4/8
<u>Common factor of 4.</u>
4/4=1
8/4=2
<u>Rewrite as a fraction.</u>
=1/2
n=1/2
<u>Divide is another option.</u>
1/2=0.5
n=1/2=0.5
- <u>Therefore, the final answer is n=1/2=0.5.</u>
I hope this helps you! Let me know if my answer is wrong or not.
Answer:
Hence the function which has the smallest minimum is: h(x)
Step-by-step explanation:
We are given function f(x) as:
- f(x) = −4 sin(x − 0.5) + 11
We know that the minimum value attained by the sine function is -1 and the maximum value attained by sine function is 1.
so the function f(x) receives the minimum value when sine function attains the maximum value since the term of sine function is subtracted.
Hence, the minimum value of f(x) is: 11-4=7 ( when sine function is equal to 1)
- Also we are given a table of values for function h(x) as:
x y
−2 14
−1 9
0 6
1 5
2 6
3 9
4 14
Hence, the minimum value attained by h(x) is 5. ( when x=1)
- Also we are given function g(x) ; a quadratic function passing through (2,7),(3,6) and (4,7)
so, the equation will be:
Hence on putting these coordinates we will get:
a=1,b=3 and c=7.
Hence the function g(x) is given as:

So,the minimum value attained by g(x) could be seen from the graph is at the point (3,6).
Hence, the minimum value attained by g(x) is 6.
Hence the function which has the smallest minimum is h(x)
<h3>47 × 63 = <u>2961</u></h3>
<h3>... Hope this will help... </h3>
<h3>U can also verify the answer using a calculator </h3>