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Cycle 1 - Lesson 6 – Rational Functions – Reciprocal of a Linear Function When you add, subtract, or multiply two polynomial functions, the result is another polynomial function. When you divide polynomial functions, the result is a RATIONAL function: where Since division by zero is undefined, rational functions have properties like asymptotes.

The basic reciprocal of a linear function Make a table of values and sketch a graph of the function

x

y

-4 -3 -2 -1 -0.5 -0.25 0 0.25 0.5 1 2 3 4 Describe what happens to the function as…

x approaches negative infinity (-∞): x approaches positive infinity (+∞): x approaches 0 from the left: x approaches 0 from the right:

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Reciprocal of a Linear function of the form: Graph the function below on Desmos and draw a sketch on the grid.

Domain:

Range:

Vertical asymptote:

Horizontal asymptote:

Describe the behaviour of the function near the vertical asymptote:

Describe the end behaviour (as x approaches ±∞):

When k < 0 in Graph the function below on Desmos and draw a sketch on the grid.

Describe the behaviour of the function near the vertical asymptote:

Describe the end behaviour (as x approaches ±∞):

How would you describe the major changes in the original function when k < 0 ?

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Example: Finding intercepts

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Cycle 1 – Lesson 6 - PRACTICE QUESTIONS

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ANSWERS

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