Podcast
Questions and Answers
What is the domain of the hyperbolic function defined by the equation $y = \frac{a}{x} + q$?
What is the domain of the hyperbolic function defined by the equation $y = \frac{a}{x} + q$?
- \{x : x \in \mathbb{R}, x > 0\}
- \{x : x \in \mathbb{R}, x \neq 0\} (correct)
- \{x : x \in \mathbb{R}\}
- \{x : x \in \mathbb{R}, x = 0\}
What happens to the graph of the hyperbolic function when $q > 0$?
What happens to the graph of the hyperbolic function when $q > 0$?
- The graph is reflected across the x-axis.
- The graph is shifted vertically upwards by $q$ units. (correct)
- No change occurs to the graph.
- The graph is shifted horizontally to the right.
What is the nature of the vertical asymptote for a hyperbolic function?
What is the nature of the vertical asymptote for a hyperbolic function?
- The line $x = 0$. (correct)
- The line $y = 0$.
- The line $y = a$.
- The line $y = q$.
When $a < 0$ in the hyperbolic function $y = \frac{a}{x} + q$, in which quadrants does the graph lie?
When $a < 0$ in the hyperbolic function $y = \frac{a}{x} + q$, in which quadrants does the graph lie?
Which of the following statements about the y-intercept of the hyperbolic function is true?
Which of the following statements about the y-intercept of the hyperbolic function is true?
To find the x-intercept of the function $y = \frac{a}{x} + q$, what equation must be solved?
To find the x-intercept of the function $y = \frac{a}{x} + q$, what equation must be solved?
Which line represents the horizontal asymptote of the hyperbolic function?
Which line represents the horizontal asymptote of the hyperbolic function?
What effect does changing $a$ from positive to negative have on the hyperbolic function's shape?
What effect does changing $a$ from positive to negative have on the hyperbolic function's shape?
What is the range of the hyperbolic function defined by the equation $y = \frac{a}{x} + q$?
What is the range of the hyperbolic function defined by the equation $y = \frac{a}{x} + q$?
Which quadrants does a hyperbolic function graph occupy if $a$ is positive?
Which quadrants does a hyperbolic function graph occupy if $a$ is positive?
What is the effect of a vertical shift when $q < 0$ in the hyperbolic function?
What is the effect of a vertical shift when $q < 0$ in the hyperbolic function?
Which of the following lines serves as the vertical asymptote for the hyperbolic function?
Which of the following lines serves as the vertical asymptote for the hyperbolic function?
How can the x-intercept of the hyperbolic function be determined?
How can the x-intercept of the hyperbolic function be determined?
What characteristics describe a hyperbolic function's y-intercept?
What characteristics describe a hyperbolic function's y-intercept?
If $q$ is greater than zero in the hyperbolic function, how does the graph behave?
If $q$ is greater than zero in the hyperbolic function, how does the graph behave?
Which of the following is a characteristic of the hyperbolic function's graph?
Which of the following is a characteristic of the hyperbolic function's graph?
What describes the axes of symmetry for the hyperbolic function?
What describes the axes of symmetry for the hyperbolic function?
How is the x-intercept of the hyperbolic function determined?
How is the x-intercept of the hyperbolic function determined?
What would happen to the graph of a hyperbolic function if $q$ is assigned a negative value?
What would happen to the graph of a hyperbolic function if $q$ is assigned a negative value?
Which statement is true regarding the horizontal asymptote of a hyperbolic function?
Which statement is true regarding the horizontal asymptote of a hyperbolic function?
For the hyperbolic function $y = rac{a}{x} + q$, when is the function considered undefined?
For the hyperbolic function $y = rac{a}{x} + q$, when is the function considered undefined?
What is the implication of a positive value for $a$ in a hyperbolic function?
What is the implication of a positive value for $a$ in a hyperbolic function?
Which statement about the range of the hyperbolic function is accurate?
Which statement about the range of the hyperbolic function is accurate?
In a hyperbolic function, how does the value of q affect the horizontal asymptote?
In a hyperbolic function, how does the value of q affect the horizontal asymptote?
What can be said about the x-intercept of the hyperbolic function?
What can be said about the x-intercept of the hyperbolic function?
Which of the following reflects the implications of a vertical asymptote for the hyperbolic function?
Which of the following reflects the implications of a vertical asymptote for the hyperbolic function?
Which of these properties would you expect for a hyperbolic function with negative value of q?
Which of these properties would you expect for a hyperbolic function with negative value of q?
What is the significance of the axes of symmetry for the hyperbolic function?
What is the significance of the axes of symmetry for the hyperbolic function?
How does the sign of the coefficient a in the hyperbolic function affect the graph?
How does the sign of the coefficient a in the hyperbolic function affect the graph?
For the hyperbolic function, how is the behavior of the function as x approaches a value of zero characterized?
For the hyperbolic function, how is the behavior of the function as x approaches a value of zero characterized?
What statement accurately describes the relationship between a and q in the hyperbolic function?
What statement accurately describes the relationship between a and q in the hyperbolic function?
If the graph of the hyperbolic function does not have an x-intercept, what can be inferred?
If the graph of the hyperbolic function does not have an x-intercept, what can be inferred?
