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Cycle 3 – Lesson 6 – Rational Functions – Linear/Linear In Cycle 1, we saw that the basic reciprocal of a linear function looks like this: Desmos activity – Slide 3 - Write the equation of a reciprocal function with a vertical asymptote at

x

1 and a horizontal asymptote at y  2 : 2

Now create a common denominator and simplify to write this function as one fraction, then check your result in Desmos.

Desmos activity – Slide 4 - Fill in the properties for this rational function: vertical asymptote:

horizontal asymptote:

x-intercept:

y-intercept:

Desmos activity – Slide 5 - Fill in the properties for this rational function: vertical asymptote:

horizontal asymptote:

x-intercept:

y-intercept:

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Example: Determine the key features and properties of the function shown below.

vertical asymptote:

horizontal asymptote:

x-intercept:

Domain:

y-intercept:

Range:

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Cycle 3 – Lesson 6 - Practice Questions – Rational Functions 6. Determine an equation for the horizontal asymptote of each function. Then, determine an equation for the vertical asymptote and graph the function. State the domain and range.

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