SOLUTION: Consider the function {{{ (3x^2-2x-4)/(x+2) }}} a) Find the equation of the slant asymptote algebraically. b) Using a graphing calculator, find the range of f(x). Explain the

Algebra ->  Rational-functions -> SOLUTION: Consider the function {{{ (3x^2-2x-4)/(x+2) }}} a) Find the equation of the slant asymptote algebraically. b) Using a graphing calculator, find the range of f(x). Explain the       Log On


   

Question 972886: Consider the function +%283x%5E2-2x-4%29%2F%28x%2B2%29+
a) Find the equation of the slant asymptote algebraically.
b) Using a graphing calculator, find the range of f(x). Explain the process you used.
Found 2 solutions by lwsshak3, solver91311:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the function +%283x%5E2-2x-4%29%2F%28x%2B2%29+
a) Find the equation of the slant asymptote algebraically.
b) Using a graphing calculator, find the range of f(x). Explain the process you used.
***
Perform long division:
.................3x........-8.................
..x+2..|.....3x^2.....-2x.......-4........
................3x^2.....6x....................
............................-8x.......-4........
............................-8x.......-16.....
.........................................12....
+%283x%5E2-2x-4%29%2F%28x%2B2%29=%283x-8%29%2B%2812%2F%28x%2B2%29%29
Equation of slant asymptote=3x-8 (Ignore remainder)
Using a graphic calculator:
Range: (-2, ∞)
see graph below:

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use polynomial long division to divide the denominator into the numerator. Set equal to the quotient (discarding any remainder) to obtain the equation of the oblique asymptote.

You can use your own graphing calculator to do part b). The range is the set of values that the function assumes for all possible values of the independent variable in the domain.

John

My calculator said it, I believe it, that settles it