Gr 11 Math Ch 5: Hyperbolic Functions

What is the effect of q > 0 on the graph of y = a/x + q?

The graph is shifted vertically upwards by q units.

What is the vertical asymptote of the function y = a/x + q?

The line x = 0.

What happens to the graph of y = a/x + q when a > 1?

The graph moves further away from the axes.

What is the effect of p > 0 on the graph of y = a/(x + p) + q?

The graph is shifted horizontally to the left by p units. Signup and view all the answers

What is the domain of the function y = a/(x + p) + q?

All real numbers except x = -p. Signup and view all the answers

What is the range of the function y = a/(x + p) + q?

All real numbers except y = q. Signup and view all the answers

What happens to the graph of y = a/x + q when a tends to 0?

The graph moves closer to the axes. Signup and view all the answers

What is the effect of a < 0 on the graph of y = a/x + q?

The graph lies in the second and fourth quadrants. Signup and view all the answers

What is the effect of a horizontal shift on the graph of y = a/(x + p) + q?

It does not change the shape of the graph. Signup and view all the answers

What is the relationship between a and the quadrant of the graph of y = a/x + q?

a > 0 implies the graph lies in the first and third quadrants. Signup and view all the answers

What is true about the graph of y = a/(x + p) + q when p = 0?

It is the same as the graph of y = a/x + q. Signup and view all the answers

What happens to the graph of y = a/x + q when a approaches infinity?

It gets further away from the y-axis. Signup and view all the answers

What is the effect of q on the graph of y = a/x + q?

It shifts the graph vertically. Signup and view all the answers

What is true about the graph of y = a/(x + p) + q when a < -1?

It is further away from the x-axis than the graph of y = -1/(x + p) + q. Signup and view all the answers

What can be said about the graph of y = a/x + q when x = -p?

The graph is undefined. Signup and view all the answers

What is the vertical asymptote of the graph of y = a/(x + p) + q?

The line x = -p. Signup and view all the answers

Which of the following statements is true about the graph of y = a/x + q when a < 0 and q > 0?

The graph is shifted upwards by q units and lies in the second and fourth quadrants. Signup and view all the answers

What is the effect of a > 1 on the graph of y = a/x + q?

The graph moves further away from the axes than y = 1/x. Signup and view all the answers

What is the effect of p > 0 on the graph of y = a/(x + p) + q?

The graph is shifted to the left by p units. Signup and view all the answers

What is the relationship between the graph of y = a/x + q and the line y = q?

The line y = q is a horizontal asymptote. Signup and view all the answers

What is true about the graph of y = a/(x + p) + q when x = -p?

The function is undefined. Signup and view all the answers

What is the effect of a < -1 on the graph of y = a/x + q?

The graph moves further away from the axes than y = -1/x. Signup and view all the answers

What is the relationship between the graph of y = a/x + q and the graph of y = a/(x + p) + q?

The two graphs have different vertical asymptotes. Signup and view all the answers

What is true about the graph of y = a/(x + p) + q when p < 0?

The graph is shifted to the right by p units. Signup and view all the answers

What is the effect of a positive value of p on the graph of y = a/(x + p) + q?

The graph is shifted horizontally to the left. Signup and view all the answers

What happens to the graph of y = a/x + q as a approaches infinity?

The graph moves further away from the axes. Signup and view all the answers

What is true about the graph of y = a/(x + p) + q when q < 0?

The graph is shifted vertically downwards. Signup and view all the answers

What is the effect of a negative value of a on the graph of y = a/x + q?

The graph lies in the second and fourth quadrants. Signup and view all the answers

What can be said about the graph of y = a/x + q when x = 0?

The graph is undefined. Signup and view all the answers

What is true about the graph of y = a/(x + p) + q when q = 0?

The graph passes through the origin. Signup and view all the answers

What is the relationship between the graph of y = a/x + q and the graph of y = -a/x - q?

They are reflections about the x-axis. Signup and view all the answers

What is true about the graph of y = a/(x + p) + q when a = 1?

The graph is a horizontal shift of y = 1/x. Signup and view all the answers

What happens to the graph of y = a/x + q when a approaches 0?

The graph becomes closer to the axes than y = 1/x. Signup and view all the answers

What is the effect of a horizontal shift on the graph of y = a/(x + p) + q?

The graph shifts horizontally. Signup and view all the answers

What is the relationship between a and the quadrants of the graph of y = a/x + q?

For a < 0, the graph lies in the second and fourth quadrants. Signup and view all the answers

What is true about the graph of y = a/(x + p) + q when p is negative?

The graph shifts to the left. Signup and view all the answers

What is the horizontal asymptote of the graph of y = a/(x + p) + q?

y = q Signup and view all the answers

Gr 11 Math Ch 5: Hyperbolic Functions

Questions and Answers

What is the effect of q > 0 on the graph of y = a/x + q?

What is the vertical asymptote of the function y = a/x + q?

What happens to the graph of y = a/x + q when a > 1?

What is the effect of p > 0 on the graph of y = a/(x + p) + q?

What is the domain of the function y = a/(x + p) + q?

What is the range of the function y = a/(x + p) + q?

What happens to the graph of y = a/x + q when a tends to 0?

What is the effect of a < 0 on the graph of y = a/x + q?

What is the effect of a horizontal shift on the graph of y = a/(x + p) + q?

What is the relationship between a and the quadrant of the graph of y = a/x + q?

What is true about the graph of y = a/(x + p) + q when p = 0?

What happens to the graph of y = a/x + q when a approaches infinity?

What is the effect of q on the graph of y = a/x + q?

What is true about the graph of y = a/(x + p) + q when a < -1?

What can be said about the graph of y = a/x + q when x = -p?

What is the vertical asymptote of the graph of y = a/(x + p) + q?

Which of the following statements is true about the graph of y = a/x + q when a < 0 and q > 0?

What is the effect of a > 1 on the graph of y = a/x + q?

What is the effect of p > 0 on the graph of y = a/(x + p) + q?

What is the relationship between the graph of y = a/x + q and the line y = q?

What is true about the graph of y = a/(x + p) + q when x = -p?

What is the effect of a < -1 on the graph of y = a/x + q?

What is the relationship between the graph of y = a/x + q and the graph of y = a/(x + p) + q?

What is true about the graph of y = a/(x + p) + q when p < 0?

What is the effect of a positive value of p on the graph of y = a/(x + p) + q?

What happens to the graph of y = a/x + q as a approaches infinity?

What is true about the graph of y = a/(x + p) + q when q < 0?

What is the effect of a negative value of a on the graph of y = a/x + q?

What can be said about the graph of y = a/x + q when x = 0?

What is true about the graph of y = a/(x + p) + q when q = 0?

What is the relationship between the graph of y = a/x + q and the graph of y = -a/x - q?

What is true about the graph of y = a/(x + p) + q when a = 1?

What happens to the graph of y = a/x + q when a approaches 0?

What is the effect of a horizontal shift on the graph of y = a/(x + p) + q?

What is the relationship between a and the quadrants of the graph of y = a/x + q?

What is true about the graph of y = a/(x + p) + q when p is negative?

What is the horizontal asymptote of the graph of y = a/(x + p) + q?

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