What is the h(x)=((x^3-4x^2-13x+24))/((x^2-7x+8)) ?

The h(x)=((x^3-4x^2-13x+24))/((x^2-7x+8)) is

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h(x)=((x^3-4x^2-13x+24))/((x^2-7x+8))

h (x) = \frac{( x ^{3} - 4 x ^{2} - 13 x + 24 )}{( x ^{2} - 7 x + 8 )}

Domain : x < \frac{7 - 17}{2} or \frac{7 - 17}{2} < x < \frac{7 + 17}{2} or x > \frac{7 + 17}{2}

Range : f (x) < \frac{7 - 17}{2} + 3 or \frac{7 - 17}{2} + 3 < f (x) < \frac{7 + 17}{2} + 3 or f (x) > \frac{7 + 17}{2} + 3

X Intercepts : (- 3, 0), Y Intercepts : (0, 3)

Asymptotes : Slant y = x + 3

Extreme Points : None

Interval Notation

Domain : (- \infty, \frac{7 - 17}{2}) \cup (\frac{7 - 17}{2}, \frac{7 + 17}{2}) \cup (\frac{7 + 17}{2}, \infty)

Range : (- \infty, \frac{7 - 17}{2} + 3) \cup (\frac{7 - 17}{2} + 3, \frac{7 + 17}{2} + 3) \cup (\frac{7 + 17}{2} + 3, \infty)

Solution steps

Domain of

\frac{x ^{3} - 4 x ^{2} - 13 x + 24}{x ^{2} - 7 x + 8} : x < \frac{7 - 17}{2} or \frac{7 - 17}{2} < x < \frac{7 + 17}{2} or x > \frac{7 + 17}{2}

Range of

\frac{x ^{3} - 4 x ^{2} - 13 x + 24}{x ^{2} - 7 x + 8} : f (x) < \frac{7 - 17}{2} + 3 or \frac{7 - 17}{2} + 3 < f (x) < \frac{7 + 17}{2} + 3 or f (x) > \frac{7 + 17}{2} + 3

Axis interception points of

\frac{x ^{3} - 4 x ^{2} - 13 x + 24}{x ^{2} - 7 x + 8} :

X Intercepts

: (- 3, 0),

Y Intercepts

: (0, 3)

Asymptotes of

\frac{x ^{3} - 4 x ^{2} - 13 x + 24}{x ^{2} - 7 x + 8} :

Slant

: y = x + 3

Extreme Points of

\frac{x ^{3} - 4 x ^{2} - 13 x + 24}{x ^{2} - 7 x + 8} :

None

f (t) = t^{2} - t + 4

f (z) = \frac{sin ( z )}{z}

f (x) = - 2 (x - 2) (x + 6)

y = 2 x + 50

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

What is the h(x)=((x^3-4x^2-13x+24))/((x^2-7x+8)) ?
The h(x)=((x^3-4x^2-13x+24))/((x^2-7x+8)) is