Rectangular Hyperbolas (VCE SSCE Mathematical Methods): Quizzes

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Rectangular hyperbolas
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Why is the function y=1xy = \frac{1}{x} undefined at x=0x = 0?

Division by zero is not allowed

What are asymptotes?

Lines the curve approaches but never touches

In which quadrants do the branches of y=1xy = \frac{1}{x} lie?

First and third quadrants

What is the vertical asymptote of y=1xy = \frac{1}{x}?

x=0x = 0

As xx \to \infty for y=1xy = \frac{1}{x}, what happens to yy?

y0+y \to 0^+

In which quadrants are the branches of y=1xy = -\frac{1}{x}?

Second and fourth quadrants

For y=1x1+3y = \frac{1}{x-1} + 3, what is the horizontal asymptote?

y=3y = 3

What transformation changes y=1xy = \frac{1}{x} to y=2xy = \frac{2}{x}?

Dilation of factor 2 from the xx-axis

For y=2x+13y = \frac{2}{x+1} - 3, what is the yy-intercept?

1-1

In y=axh+ky = \frac{a}{x-h} + k, what does the parameter hh determine?

Horizontal shift

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