3.1 and 3.2 Relations and Functions

Which of the following statements is NOT ​true? A. A function can have several​ y-intercepts. B. Another name for an​ x-intercept is a real zero. C. A function can have infinitely many​ x-intercepts. D. Every function can be represented by a graph in the Cartesian plane.

A. A function can have several y-intercepts.

Which of the following statements best defines a relative maximum of a function y=f(x)? A. When a function changes from increasing to decreasing at a point (c, f(c)), then f is said to have a relative maximum at x=c. B. When a function changes from decreasing to increasing at a point (c, f(c)), then f is said to have a relative maximum at x= f(c). C. When a function changes from decreasing to increasing at a point (c, f(c)), then f is said to have a relative maximum at x=c D. When a function changes from increasing to decreasing at a point (c, f(c)), then f is said to have a relative maximum at x=f(c).

A. When a function changes from increasing to decreasing at a point (c, f(c)), then f is said to have a relative maximum at x=c.

For a number a to be in the domain of a function y=f(x), _______________. A. f(a) must be defined. B. f(a) must be a rational number. C. f(a) must be a number greater than or equal to 0. D. f(a) must be an integer.

A. f(a) must be defined.

Which of the following statements is true? A. A function y=f(x) is even if for every point (x,y) on the graph of f, the point (x,-y) also lies on the graph of f. B. A function y=f(x) is odd if for every point (x,y) on the graph of f, the point (-x,-y) also lies on the graph of f. C. The graph of every odd function is symmetric about the y-axis. D. The graph of every even function is symmetric about the origin.

B. A function y=f(x) is odd if for every point (x,y) on the graph of f, the point (-x,-y) also lies on the graph of f.

Which of the following statements is​ true? A. The domain of a function must always be the same as the range of a function. B. If a rational function has a vertical​ asymptote, then the domain of the function can never be (−∞, ∞). C. If the domain of a function is the interval (a, b] for real numbers a<b, then the line x=a must be a vertical asymptote. D. If the domain of a function is (−∞, ∞), then the function cannot have a horizontal asymptote.

B. If a rational function has a vertical​ asymptote, then the domain of the function can never be (−∞, ∞).

Which of the following statements is not ​true? A. If the domain and range of a relation are sets of real​ numbers, then the relation can be represented by plotting ordered pairs in the Cartesian plane. B. If the domain of a function consists of more than one​ element, then the range must also consist of more than one element. C. Two or more distinct elements in the domain of a function can correspond to the same element in the range. D. Every function is a relation but not every relation is a function.

B. If the domain of a function consists of more than one​ element, then the range must also consist of more than one element.

Which of the following statements defines a​ function? A. A function is a relation such that for each element in the​ domain, there is at least one corresponding element in the range. B. A function is a relation such that for each element in the​ range, there is at least one corresponding element in the domain. C. A function is a relation such that for each element in the​ domain, there is exactly one corresponding element in the range. D. A function is a relation such that for each element in the​ range, there is exactly one corresponding element in the domain.

C. A function is a relation such that for each element in the​ domain, there is exactly one corresponding element in the range.

Which of the following statements is true? A. A function is increasing on an interval (a,b) if, for any x1 and x2 chosen from the interval with x1 > x2, then f(x1) < f(x2). B. A function is decreasing on an interval (a,b) if, for any x1 and x2 chosen from the interval with x1 > x2, then f(x1) > f(x2). C. A function is decreasing on an interval (a,b) if, for any x1 and x2 chosen from the interval with x1 < x2, then f(x1) < f(x2). D. A function is increasing on an interval (a,b) if, for any x1 and x2 chosen from the interval with x1 < x2, then f(x1) < f(x2).

D. A function is increasing on an interval (a,b) if, for any x1 and x2 chosen from the interval with x1 < x2, then f(x1) < f(x2).

Which of the following statements is true? A. A graph in the Cartesian plane is the graph of a function if every vertical line intersects the graph at least once. B. A graph in the Cartesian plane is the graph of a function if every horizontal line intersects the graph no more than once. C. The graph of a horizontal line in the Cartesian plane cannot represent a function. D. A graph in the Cartesian plane is the graph of a function if every vertical line intersects the graph no more than once.

D. A graph in the Cartesian plane is the graph of a function if every vertical line intersects the graph no more than once.

Which of the following statements defines a​ relation? A. A relation is a correspondence between two sets A and B such that each element of set A equals exactly one element in set B. B. A relation is a correspondence between two sets A and B such that each element of set A corresponds to exactly one element in set B. C. A relation is a correspondence between two sets A and B such that each element of set A equals one or more elements in set B. D. A relation is a correspondence between two sets A and B such that each element of set A corresponds to one or more elements in set B.

D. A relation is a correspondence between two sets A and B such that each element of set A corresponds to one or more elements in set B.

Which of the following statements is NOT true? A. If n≥2 is an even integer, then the domain of: " f(x) = the n root of g(x) " is the solution to the inequality g(x) greater than or equal to 0. B. The domain of every polynomial function is all real numbers. C. Many functions have restricted domains. D. If n≥2 is an odd integer, then the domain of: " f(x) = the n root of g(x) " is the solution to the inequality g(x) greater than or equal to 0.

D. If n is greater than or equal to 2 is an odd integer, then the domain of: " f(x) = the n root of g(x) " is the solution to the inequality g(x) greater than or equal to 0.