2 Reciprocals of Quadratic Functions PDF

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Reciprocal of a Quadratic Function

Learning Goal: By the end of this lesson, students will have gone through all the major characteristics of the reciprocal of a quadratic function. They will practice graphing them as well as determining the equation of the function from key points. Examples: 1. 𝑦 =

1 (𝑥−3)(𝑥+1)

a. graph

b. the domain

c. the range

d. 𝑥-intercept(s)

e. 𝑦-intercept(s)

f.

all asymptotes

g. the behaviour of the function at the vertical asymptote

h. the end behaviour of the function

i.

the behaviour of the graph by completing the table below:

Interval Sign of y Sign of slope Change in slope

Work: pg. 165 (3, 5, 8defg, 11, 13)

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Reciprocal of a Quadratic Function

2. 𝑦 =

3 𝑥 2+𝑥−2

a. graph

b. the domain

c. the range

d. 𝑥-intercept(s)

e. 𝑦-intercept(s)

f.

all asymptotes

g. the behaviour of the function at the vertical asymptote

h. the end behaviour of the function

i.

the behaviour of the graph by completing the table below:

Interval Sign of y Sign of slope Change in slope

Work: pg. 165 (3, 5, 8defg, 11, 13)

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Reciprocal of a Quadratic Function 2

3. 𝑦 = − 2𝑥 2−5𝑥−3 a. graph

b. the domain

c. the range

d. 𝑥-intercept(s)

e. 𝑦-intercept(s)

f.

all asymptotes

g. the behaviour of the function at the vertical asymptote

h. the end behaviour of the function

i.

the behaviour of the graph by completing the table below:

Interval Sign of y Sign of slope Change in slope

Work: pg. 165 (3, 5, 8defg, 11, 13)

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Reciprocal of a Quadratic Function

4. 𝑦 =

1 (𝑥+2)2

a. graph

b. the domain

c. the range

d. 𝑥-intercept(s)

e. 𝑦-intercept(s)

f.

all asymptotes

g. the behaviour of the function at the vertical asymptote

h. the end behaviour of the function

i.

the behaviour of the graph by completing the table below:

Interval Sign of y Sign of slope Change in slope

Work: pg. 165 (3, 5, 8defg, 11, 13)

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Reciprocal of a Quadratic Function

5. 𝑦 =

1 𝑥 2+2

a. graph

b. the domain

c. the range

d. 𝑥-intercept(s)

e. 𝑦-intercept(s)

f.

all asymptotes

g. the behaviour of the function at the vertical asymptote

h. the end behaviour of the function

i.

the behaviour of the graph by completing the table below:

Interval Sign of y Sign of slope Change in slope

Work: pg. 165 (3, 5, 8defg, 11, 13)

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Reciprocal of a Quadratic Function

2. Determine a possible equation to represent each function on the grids below, if each is the reciprocal of a quadratic function. a) b)

3. The apparent brightness of a light source is inversely proportional to the square of the distance from the light source. At a distance of 2.4 m, the brightness of a particular light source is 500 lux. a. Determine an equation relating the brightness of the light source and the distance from the source. b. Sketch a graph of this relationship. c. What is the distance of the light source at a distance of 12 m? d. Determine the range of distances for which the brightness of the light source is less than 100 lux.

Work: pg. 165 (3, 5, 8defg, 11, 13)...