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The reciprocal is basic the numerator and denominator flipped
For example: If we have a fraction 1/3, then the reciprocal will be 3/1, if we have a 3/4, we will have 4/3.

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The main formula of the reciprocal of the quadratic function is y = 1/x^2, and x can not be 0.

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The main formula of the reciprocal of the quadratic function is y = 1/x^2, and x can not be 0.

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Rational functions can be analysed using key features: asymptotes, intercepts, slope (positive or negative, increasing or decreasing), domain, range, and positive and negative intervals.

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Rational functions can be analysed using key features: asymptotes, intercepts, slope (positive or negative, increasing or decreasing), domain, range, and positive and negative intervals.

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Example question 1: Consider the function f(x) = 2/x^2 - 4

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Example question 1: Consider the function f(x) = 2/x^2 - 4

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a) State the domain
b) Find the equation of the asymptotes
c) Describe the behaviour of the function near the asymptotes.

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a) Factor the denominator
x^2 - 4 = (x+2)(x-2)
State the restrictions
x doesn’t = 2, -2
Domain: {x doesn’t = 2, -2 | xER}

b) Vertical asymptotes x= 2, -2
Horizontal asymptote y = 0

c) look at the image

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Question 2: stretch the previous equation

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Question 2: stretch the previous equation

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Lets see a example with the equation y = x^2, so the reciprocal is y=1/x^2

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Lets see a example with the equation y = x^2, so the reciprocal is y=1/x^2

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1. There are no zeros, so no vertical asymptotes.

2. The quadratic is positive, so the reciprocal will also always be positive.

3. The y-intercept of
y = x^2 is 0, so the reciprocal at this point is undefined.

4. As x becomes very large or very small, y approaches 0.

5. The vertex of
y = x^2 is at (0,0), which means the reciprocal function has a minimum value at x = 0, but it is not defined at this point.

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Reciprocals of quadratic functions with two zeros have three parts, with the middle one reaching a maximum or minimum point. This point is equidistant from the two vertical asymptotes.

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Reciprocals of quadratic functions with two zeros have three parts, with the middle one reaching a maximum or minimum point. This point is equidistant from the two vertical asymptotes.