Hyperbolic Functions (Grade 10 NSC Matric Mathematics): Quizzes

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Hyperbolic Functions
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What is the general form of a hyperbolic function?

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

What is the domain of y=ax+qy = \frac{a}{x} + q?

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

What is the range of y=ax+qy = \frac{a}{x} + q?

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

What is the vertical asymptote for any hyperbolic function y=ax+qy = \frac{a}{x} + q?

x=0x = 0

For g(x)=2x+2g(x) = \frac{2}{x} + 2, what is the horizontal asymptote?

y=2y = 2

When a>0a > 0, in which quadrants does the hyperbola lie?

First and third quadrants

When a<0a < 0, in which quadrants does the hyperbola lie?

Second and fourth quadrants

What is the x-intercept of y=−4x+7y = \frac{-4}{x} + 7?

(47,0)\left(\frac{4}{7}, 0\right)

Does a hyperbolic function have a y-intercept?

No, it's undefined at x=0x = 0

What effect does the parameter qq have on the graph?

Causes a vertical shift

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