What is the range of (x^2+x-12)/(x-3) ?

The range of (x^2+x-12)/(x-3) is f(x) 7

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range of (x^2+x-12)/(x-3)

range

\frac{x ^{2} + x - 12}{x - 3}

f (x) < 7 or f (x) > 7

Interval Notation

(- \infty, 7) \cup (7, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{x ^{2} + x - 12}{x - 3} : x < 3 or x > 3

Simplify

\frac{x ^{2} + x - 12}{x - 3} : x + 4

Extreme Points of

x + 4 :

None

Find the range for the interval

- \infty < x < 3 : - \infty < f (x) < 7

Find the range for the interval

3 < x < \infty : 7 < f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) < 7 or f (x) > 7

f (x) < 7 or f (x) > 7

\frac{3 x}{( x + 2 ) ^{2}}

y = 4 x^{2} + 8 x - 1

f (x) = \frac{x + 2}{x - 2}

f (x) = 2 x^{2} + 4 x + 3

f (x) = \frac{1}{x ^{2} - 5 x + 6}

What is the range of (x^2+x-12)/(x-3) ?
The range of (x^2+x-12)/(x-3) is f(x)<7\lor f(x)>7