vertical asymptotes y-intercepts of rational functions horizontal asymptotes domain of rational...

Vertical Asymptote

s

Y-intercept

s of Rational

Functions

Horizontal Asymptot

es

Domain of Rational

Functions

Factoring when a =

1

Factoring when a>1

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JJΣθPARδYΣθPARδY!! MαthMαth

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Rational Rational Functions/Factoring Functions/Factoring

JΣθPARδY!JΣθPARδY!

Vertical Asymptotes - 100

• Determine the location of the vertical asymptote(s) of

x = 2

JJΣθPARδYΣθPARδY!! MαthMαth

Vertical Asymptotes - 200

• Determine the location of the vertical asymptote(s) of

JJΣθPARδYΣθPARδY!! MαthMαth

x = -5

Vertical Asymptotes - 300

• Use the graph to determine the vertical asymptotes

JJΣθPARδYΣθPARδY!! MαthMαth

x = -5

Vertical Asymptotes - 400

• Use the table and graph to determine the vertical asymptote(s)

JJΣθPARδYΣθPARδY!! MαthMαth

Vertical Asymptote at x = -4

Y-intercepts - 100

• Find the y-intercept of the rational function

JJΣθPARδYΣθPARδY!! MαthMαth

(0, 5)

Y-intercepts - 200

• Find the y-intercept of the rational function

JJΣθPARδYΣθPARδY!! MαthMαth

(0, -6)

Y-intercepts - 300

• Find the y-intercept of the rational function

JJΣθPARδYΣθPARδY!! MαthMαth

(0, 0.375)

Y-intercepts - 400

• Find the y-intercept of the rational function

JJΣθPARδYΣθPARδY!! MαthMαth

(0, 1.5)

Horizontal Asymptotes - 100

• Determine the horizontal asymptote of the following rational function.

JJΣθPARδYΣθPARδY!! MαthMαth

y = 0

Horizontal Asymptotes - 200

• Determine the horizontal asymptote of the following rational function.

JJΣθPARδYΣθPARδY!! MαthMαth

y = 6

Horizontal Asymptotes - 300

• Determine the horizontal asymptote of the following rational function.

JJΣθPARδYΣθPARδY!! MαthMαth

y = 1

Horizontal Asymptotes - 400

• Determine the horizontal asymptote of the following rational function.

JJΣθPARδYΣθPARδY!! MαthMαth

No Horizontal Asymptote

Domain - 100

• What is the theoretical domain of the following rational function?

JJΣθPARδYΣθPARδY!! MαthMαth

All real numbers except x = -6

Domain - 200

• What is the theoretical domain of the following rational function?

JJΣθPARδYΣθPARδY!! MαthMαth

All real numbers except x = 2

• What is the theoretical domain of the following rational function?

Domain - 300

JJΣθPARδYΣθPARδY!! MαthMαth

All real numbers except x = 1

Domain - 400

• What is the practical domain of the rational equation

JJΣθPARδYΣθPARδY!! MαthMαth

Practical domain can only be determined within a specific scenario. Context must be present in order to determine practical domain. The theoretical domain of this function is all real numbers except d = 0.

Factoring a = 1 - 100

• Write the following in factored form

JJΣθPARδYΣθPARδY!! MαthMαth

(x + 4)(x + 5)

Factoring a = 1 - 200

• Write the following in factored form

JJΣθPARδYΣθPARδY!! MαthMαth

(x – 4)(x + 3)

Factoring a = 1 - 300

• Write the following in factored form

JJΣθPARδYΣθPARδY!! MαthMαth

(x – 8)(x – 2)

Factoring a = 1 - 400

• Write the following in factored form

JJΣθPARδYΣθPARδY!! MαthMαth

(x + 6)(x – 6)

Factoring a > 1 - 100

• Write the following in factored form

JJΣθPARδYΣθPARδY!! MαthMαth

(2x + 1)(x – 3)

Factoring a > 1 - 200

• Write the following in factored form

JJΣθPARδYΣθPARδY!! MαthMαth

(3x + 1)(x – 4)

Factoring a > 1 - 300

• Write the following in factored form

JJΣθPARδYΣθPARδY!! MαthMαth

(5p + 9)(p – 2)

Factoring a > 1 - 400

• Write the following in factored form

JJΣθPARδYΣθPARδY!! MαthMαth

k(7k + 9)