Hyperbolic Functions (Grade 11 NSC Matric Mathematics): Quizzes

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Hyperbolic Functions
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In which quadrants does y=5x+2+3y = \frac{5}{x+2} + 3 lie?

First and third

In which quadrants does y=−4x−1+2y = \frac{-4}{x-1} + 2 lie?

Second and fourth

For y=ax+3+qy = \frac{a}{x+3} + q, which direction does the graph shift?

3 units left

What is the vertical asymptote of y=2x−5+1y = \frac{2}{x-5} + 1?

x=5x = 5

What is the horizontal asymptote of y=3x+2−4y = \frac{3}{x+2} - 4?

y=−4y = -4

What value is excluded from the domain of f(x)=1x+7+2f(x) = \frac{1}{x+7} + 2?

x=−7x = -7

What value is excluded from the range of g(x)=5x−1+6g(x) = \frac{5}{x-1} + 6?

y=6y = 6

To find the y-intercept of a hyperbola, what should you do?

Set x=0x = 0 and solve for yy

Where do the axes of symmetry intersect for y=ax+p+qy = \frac{a}{x+p} + q?

At point (−p;q)(-p; q)

What happens as ∣a∣|a| increases in y=ax+qy = \frac{a}{x} + q?

Branches move further from both axes

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