Graphs of Functions (Edexcel A-Level Mathematics): Quizzes

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Reciprocal Graphs - Sketching
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What is the basic form of a reciprocal graph?

y=kxy = \frac{k}{x}

What type of relationship do reciprocal graphs illustrate?

Inverse relationships

What does asymptotic behaviour mean?

Graph approaches a line but never touches

For y=kxy = \frac{k}{x}, where is the vertical asymptote?

x=0x = 0

For y=kax+by = \frac{k}{ax + b}, how do you find the vertical asymptote?

Set ax+b=0ax + b = 0

For y=kxy = \frac{k}{x}, where is the horizontal asymptote?

y=0y = 0

What type of symmetry does y=kxy = \frac{k}{x} have?

Symmetric about the origin

If k>0k > 0 for y=kxy = \frac{k}{x}, which quadrants contain the graph?

First and third

If k<0k < 0 for y=kxy = \frac{k}{x}, which quadrants contain the graph?

Second and fourth

For y=3x2y = \frac{3}{x - 2}, where is the vertical asymptote?

x=2x = 2

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