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Cycle 1 - Lesson 7 – Rational Functions – Reciprocal of a Quadratic Function In Lesson 6, the rational functions you analyzed had linear denominators. However, rational functions can have polynomials of any degree in the numerator and denominator. In this lesson, you will analyze and graph functions such as

Because quadratics have possibly zero, one, or two x-intercepts, a parabolic shape, and a maximum or minimum point, plotting their reciprocals becomes fairly complex.

Desmos Investigation #1 – The basic reciprocal of a quadratic function Make a table of values and sketch a graph of the function

x

y

-3 -2 -1 -0.5 0 0.5 1 2 3 Horizontal asymptote:

Vertical asymptote:

x-intercepts:

y-intercept:

Domain:

Range:

End behaviour: as x +∞

as x-∞

Positive and negative intervals: Increasing and decreasing intervals:

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Desmos Investigation #2 – Reciprocal of a Quadratic function in factored form Graph the functions below on Desmos and draw sketches on the grids.

Domain:

Range:

Domain:

Range:

Vertical asymptote(s):

Horizontal asymptote:

Vertical asymptote(s):

Horizontal asymptote:

Desmos Investigation #3 – Reciprocal of a Quadratic function in standard form Factor each denominator, then graph the functions on Desmos and sketch them below. =

=

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Desmos Investigation #4 – Reciprocal of a Quadratic function – No real roots in denominator

Domain:

Range:

Vertical asymptote(s):

Horizontal asymptote:

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Cycle 1 – Lesson 7 - PRACTICE QUESTIONS

ANSWERS