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Popular >

f(x)=(x^2-5x+6)/(x^2-2x+3)

Solution

f (x) = \frac{x ^{2} - 5 x + 6}{x ^{2} - 2 x + 3}

Solution

Domain : - \infty < x < \infty

Range : - \frac{3}{2 2} + 1 \leq f (x) \leq \frac{3}{2 2} + 1

X Intercepts : (3, 0), (2, 0), Y Intercepts : (0, 2)

Asymptotes : Horizontal y = 1

Extreme Points : Maximum (1 - 2, \frac{4 + 3 2}{4}), Minimum (1 + 2, \frac{4 - 3 2}{4})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{3}{2 2} + 1, \frac{3}{2 2} + 1]

Solution steps

Domain of

\frac{x ^{2} - 5 x + 6}{x ^{2} - 2 x + 3} : - \infty < x < \infty

Range of

\frac{x ^{2} - 5 x + 6}{x ^{2} - 2 x + 3} : - \frac{3}{2 2} + 1 \leq f (x) \leq \frac{3}{2 2} + 1

Axis interception points of

\frac{x ^{2} - 5 x + 6}{x ^{2} - 2 x + 3} :

X Intercepts

: (3, 0), (2, 0),

Y Intercepts

: (0, 2)

Asymptotes of

\frac{x ^{2} - 5 x + 6}{x ^{2} - 2 x + 3} :

Horizontal

: y = 1

Extreme Points of

\frac{x ^{2} - 5 x + 6}{x ^{2} - 2 x + 3} :

Maximum

(1 - 2, \frac{4 + 3 2}{4}),

Minimum

(1 + 2, \frac{4 - 3 2}{4})

Popular Examples

y = sec (x^{2})

y=x^3+2x^2-4x-8

y = x^{3} + 2 x^{2} - 4 x - 8

f(j)=j^2-13j+42

f (j) = j^{2} - 13 j + 42

g (x) = x - 2

y = - 4 x + 20

Frequently Asked Questions (FAQ)

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