What is the f(x)=(sqrt(2x+5))/(x^2+4x+3) ?

The f(x)=(sqrt(2x+5))/(x^2+4x+3) is

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f(x)=(sqrt(2x+5))/(x^2+4x+3)

f (x) = \frac{2 x + 5}{x ^{2} + 4 x + 3}

Domain : - \frac{5}{2} \leq x < - 1 or x > - 1

X Intercepts : (- \frac{5}{2}, 0), Y Intercepts : (0, \frac{5}{3})

Asymptotes : Vertical x = - 1

Extreme Points : Maximum (- \frac{5}{2}, 0)

Interval Notation

Domain : [- \frac{5}{2}, - 1) \cup (- 1, \infty)

Solution steps

Domain of

\frac{2 x + 5}{x ^{2} + 4 x + 3} : - \frac{5}{2} \leq x < - 1 or x > - 1

Axis interception points of

\frac{2 x + 5}{x ^{2} + 4 x + 3} :

X Intercepts

: (- \frac{5}{2}, 0),

Y Intercepts

: (0, \frac{5}{3})

Asymptotes of

\frac{2 x + 5}{x ^{2} + 4 x + 3} :

Vertical

: x = - 1

Extreme Points of

\frac{2 x + 5}{x ^{2} + 4 x + 3} :

Maximum

(- \frac{5}{2}, 0)

f (x) = - x^{2} + 15 x - 56

y = \frac{x ^{4}}{16} + \frac{1}{2 x ^{2}}

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

y = ln (sin (e^{x}))

f (x) = \frac{x ^{3} + 1}{x ^{2} - 5 x - 14}