SOLUTION: I don't understand this can someone please help me asap....Analyze the graph of the function F(x)=(x^2-7x-8)/(x+4). Write​ F(x) in lowest terms.

Algebra ->  Rational-functions -> SOLUTION: I don't understand this can someone please help me asap....Analyze the graph of the function F(x)=(x^2-7x-8)/(x+4). Write​ F(x) in lowest terms.       Log On


   

Question 1157922: I don't understand this can someone please help me asap....Analyze the graph of the function F(x)=(x^2-7x-8)/(x+4). Write​ F(x) in lowest terms.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
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F(x)=(x^2-7x-8)/(x+4)

F%28x%29=%28x%5E2-7x-8%29%2F%28x%2B4%29
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F%28x%29=%28%28x%2B1%29%28x-8%29%29%2F%28x%2B4%29
Rational function with zeros at x for -1 and +8; and undefined for x at -4. Vertical asymptote for x at -4.

Critical x values are -4, -1, +8.
Decreasing toward the left of x at -4.
Increasing for F toward the right as x goes unbound above 8 .

Oblique asymptote,...
-4    |      1      -7     -8
      |             -4     44
      |----------------------------
             1     -11     36

x-11%2B36%2F%28x%2B4%29

When x is extremely great or extremely less, F approaches line y=x-11, the oblique asymptote.


graph%28400%2C400%2C-30%2C12%2C-30%2C12%2C%28x%5E2-7x-8%29%2F%28x%2B4%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
F%28x%29=%28x%5E2-7x-8%29%2F%28x%2B4%29
F%28x%29=%28x%5E2%2Bx-8x-8%29%2F%28x%2B4%29
F%28x%29=%28%28x%5E2%2Bx%29-%288x%2B8%29%29%2F%28x%2B4%29
F%28x%29=%28x%28x%2B1%29-8%28x%2B1%29%29%2F%28x%2B4%29
F%28x%29=%28%28x-8%29%28x%2B1%29%29%2F%28x%2B4%29

x-intercepts: set F%28x%29=0
%28%28x-8%29%28x%2B1%29%29%2F%28x%2B4%29
=>x=8 and x=-1
x-intercepts at: (8,0), (-1,0)

y-intercepts: set F%28x%29=y and x=0
y=%28%280-8%29%280%2B1%29%29%2F%280%2B4%29
y=%28-8%2A1%29%2F4
y=-2
y-intercept at: (0,-2)

critical points: values of x for which is f’%28x%29=0
F'%28x%29+=+%28x%5E2+%2B+8+x+-+20%29%2F%28x+%2B+4%29%5E2
=> +%28x%5E2+%2B+8+x+-+20%29%2F%28x+%2B+4%29%5E2=0...only if numerator equal to zero
=> %28x+%2B+10%29+%28x+-+2%29=0
=>x=-10, x=2

vertical asymptote: x=-4 (makes denominator zero)
Calculate the limits:
lim%28x-%3Einfinity%2C%28x%5E2-7x-8%29%2F%28x%2B4%29%29=infinity+
lim%28x-%3E-infinity%2C%28x%5E2-7x-8%29%2F%28x%2B4%29%29=-infinity+

Thus, there are no+horizontal+asymptotes.

Do polynomial long division:
..........(x-11
x%2B4|x%5E2-7x-8
..........x%5E2%2B4x......subtract
............... -11x-8
............... -11x-44......subtract
.............................+36
The rational term approaches 0 as the variable approaches+infinity.
Thus, the slant asymptote is: x-11

to find max and min, plug in critical pointsx=-10, x=2
at x+=+-10->max
at+x+=+2->minimum