Hyperbolic Functions (Grade 10 NSC Matric Mathematics): Flashcards

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Hyperbolic Functions
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General form of hyperbolic functions

y=ax+qy = \frac{a}{x} + q where a≠0a \neq 0

Domain of y=ax+qy = \frac{a}{x} + q

{x:x∈R,x≠0}\{x : x \in \mathbb{R}, x \neq 0\}

Range of y=ax+qy = \frac{a}{x} + q

{y:y∈R,y≠q}\{y : y \in \mathbb{R}, y \neq q\}

Vertical asymptote of hyperbolic function

x=0x = 0

Horizontal asymptote of y=ax+qy = \frac{a}{x} + q

y=qy = q

Does y=ax+qy = \frac{a}{x} + q have a y-intercept?

No, it is undefined at x=0x = 0

x-intercept of y=ax+qy = \frac{a}{x} + q (when q≠0q \neq 0)

x=−aqx = -\frac{a}{q}

Effect of parameter qq on hyperbolic function

Vertical shift (up if q>0q > 0, down if q<0q < 0)

Quadrants when a>0a > 0 in y=ax+qy = \frac{a}{x} + q

First and third quadrants

Quadrants when a<0a < 0 in y=ax+qy = \frac{a}{x} + q

Second and fourth quadrants

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