Transforming reciprocal functions

DO NOW

Suppose x and y vary inversely, find y when x = 10

Assignment #59 Pg. 503, #11-17 odd

Combined Variation

Learning Target I can graph a reciprocal function, and

transform it

I can stretch, compress and reflect reciprocal functions

Success Criteria

Reciprocal Functions

Same as the inverse function

Only difference is that now we are now adding to, subtracting from and multiplying the function by things.

Parent Function of Reciprocal Function

Parent Function: Same as the inverse function We transform the parent function with the same a, h ,

and k as we would any other function (parabola, linear, exponential)

General Form of Reciprocal

Limitation: x ≠ h a: stretches and compresses h: moves function left and right k: moves function up and down

Vocabulary

Branch

Branch x-axis is horizontal asymptote

y-axis is vertical asymptote

Stretch: Graph by making tables. State the

domain and range. Key: You need several positive and negative x-

values to complete your graph

x y

-4 -1/2

-3 -2/3

-2 -1

-1 -2

x y

1 2

2 1

3 2/3

4 1/2

Stretch: Continued

x-intercept: y-intercept: Asymptotes:

Compress: Graph by making tables. State the

domain and range. Key: You need several positive and negative x-

values to complete your graph

x y

-2 -1/4

-1 -1/2

-1/2 -1

-1/4 -2

x y

1/4 2

1/2 1

1 1/2

2 1/4

Compress: Continued

x-intercept: y-intercept: Asymptotes:

Reflect: Graph by making tables. State the

domain and range. Key: You need several positive and negative x-

values to complete your graph

x y

-3 1/3

-2 1/2

-1 1

-1/2 2

x y

1/2 -2

1 -1

2 -1/2

3 -1/3

Reflect: Continued

x-intercept: y-intercept: Asymptotes:

x y

-3 1/3

-2 1/2

-1 1

-1/2 2

x y

1/2 -2

1 -1

2 -1/2

3 -1/3

DO NOW Identify the asymptotes, and domain

and range for the following graphs.

1. 2.

Learning Target I can graph a reciprocal function, and

transform it

I can translate a reciprocal function, up and down, right and left.

Success Criteria

Horizontal Shift: Graph by making tables. State the

domain and range. Key: You need several positive and negative x-

values to complete your graph

1

1

x

y

x y

-4 -1/3

-3 -1/2

-2 -1

-1 ERR

0 1

1 1/2

2 1/3

Horizontal Shift: Continued

x-intercept: y-intercept: Asymptotes:

x y

-4 -1/3

-3 -1/2

-2 -1

-1 ERR

0 1

1 1/2

2 1/3

Vertical Shift: Graph by making tables. State the

domain and range. Key: You need several positive and negative x-

values to complete your graph

21

x

y

x y

-2 1/2

-1 1

-1/2 0

0 ERR

1/2 4

1 5

2 5/2

Vertical Shift: Continued

x-intercept: y-intercept: Asymptotes:

x y

-2 1/2

-1 1

-1/2 0

0 ERR

1/2 4

1 5

2 5/2

Multiple Shifts: Graph by

making tables. State

the domain and range. Key: You need several

positive and negative x-values to complete your graph

21

1

x

yx y

-2 -7/3 = -2.33

-1 -5/2 =- 2.5

0 -3

1/2 -4

1 ERR

3/2 0

2 -1

3 -3/2 = -1.5

5 -7/4 = -1.75

Multiple Shifts: Continued

x-intercept: y-intercept: Asymptotes:

x y

-2 -7/3 = -2.33

-1 -5/2 =- 2.5

0 -3

1/2 -4

1 ERR

3/2 0

2 -1

3 -3/2 = -1.5

5 -7/4 = -1.75

Coming up with equation from asymptotes Write an equation for the translation of

with the given asymptotes1. x = 0 and y = 2

2. x = 1 and y = 0

3. x = -2 and y = 4

𝒚=𝟏𝒙

+𝟐

𝒚=𝟏

𝒙 −𝟏

𝒚=𝟏

𝒙+𝟐+𝟒

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