Test 2 Multiple Choice-Dual Enrollment Math

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

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

Which of the following statements is not ​true? Choose the incorrect statement below. A. The rectangular coordinate system is divided into four quadrants labeled as quadrants​ I, II,​ III, and IV. B. Given an ordered pair of the form​ (x,y), y is called the coordinate. C. Given an ordered pair of the form​ (x,y), x is called the abscissa. D. The rectangular coordinate system is also called the Cartesian coordinate system.

B. Given an ordered pair of the form​ (x,y), y is called the coordinate.

Given two points which represent the endpoints of the diameter of a​ circle, which of the following statements is​ true? A. The y​-coordinate of the center of the circle must be the same as at least one of the y​-coordinates of the given endpoints of the diameter. B. The center of the circle cannot be found without additional information. C. The center of the circle is the midpoint of the given endpoints of the diameter. D. The x​-coordinate of the center of the circle must be the same as at least one of the x​-coordinates of the given endpoints of the diameter.

C. The center of the circle is the midpoint of the given endpoints of the diameter.

Which of the following statements is true about the equation y equals by=b​? A. The equation y=b is the equation of a vertical line with zero slope. B. The equation y=b is the equation of a vertical line with undefined slope. C. The equation y=b is the equation of a horizontal line with zero slope. D. The equation y=b is the equation of a horizontal line with undefined slope.

C. The equation y=b is the equation of a horizontal line with zero slope.

Which of the following statements is not ​true? Choose the incorrect statement below. A. If two distinct nonvertical lines are​ parallel, then the two lines must have the same slope. B. The ratios of the vertical rise to the horizontal run of any two distinct nonvertical parallel lines must be equal. C. Given any two distinct lines in the Cartesian​ plane, the two lines will either intersect or they will be parallel. D. Given any two distinct lines in the Cartesian​ plane, the two lines will either be parallel or perpendicular.

D. Given any two distinct lines in the Cartesian​ plane, the two lines will either be parallel or perpendicular.

Which of the following statements is not​ true? Choose the incorrect statement below. A. The Pythagorean theorem is used to derive the distance formula. B. For any real numbers x1 and x2​, the absolute value of x2−x1 squared is equivalent to the expression (x2−x1)^2. C. The distance between two points is always greater than or equal to zero. D. It is possible for the distance between two points to be negative.

D. It is possible for the distance between two points to be negative.

Given that the points (x1,y1) and (x2,y2) are endpoints of a line​ segment, which of the following statements is​ true? A.The x​-coordinate of the midpoint of the line segment can be found by first taking the difference between x2 and x1 and then dividing the difference by two. B. The x​-coordinate of the midpoint of the line segment can be found by taking the difference between x2 and x1. C. The x​-coordinate of the midpoint of the line segment can be found by taking the sum of x2 and x1. D. The x​-coordinate of the midpoint of the line segment can be found by first taking the sum of x2 and x1 and then dividing the sum by two.

D. The x​-coordinate of the midpoint of the line segment can be found by first taking the sum of x2 and x1 and then dividing the sum by two.

Which of the following statements is not​ true? Choose the incorrect statement below. A. A system of linear equations in two variables must have at least one solution. B. It is possible for a system of linear equations in two variables to have infinitely many solutions. C. The solution to a system of equations in two variables is the set of all ordered pairs for which both equations are true. D. A system of linear equations in two variables is the collection of two linear equations in two variables considered simultaneously.

A. A system of linear equations in two variables must have at least one solution.

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

A. If n≥2 is an odd​ integer, then the domain of f(x)= nroot of g(x)is the solution to the inequality g(x)≥0.

Which of the following equations is in​ point-slope form? A. y−y1=m(x−x1) B. y=mx+b C. m= x2−x1 / y2−y1 D. Ax+By=C

A. y−y1=m(x−x1)

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 an integer. D. ​f(a) must be a number greater than or equal to 0.

A. ​f(a) must be defined.

Given the equation of a line in standard​ form, Ax+By=C with B not equals≠​0, which of the following represents the slope of this​ line? A. m= C/B B. m= −A/B C. m= A/B D. m= -B/A

B. m= −A/B

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

C. A function can have several​ y-intercepts.

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 one or more elements in set B. B. 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. C. 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 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 corresponds to one or more elements in set B.

Which of the following statements is not ​true? A. Two or more distinct elements in the domain of a function can correspond to the same element in the range. B. Every function is a relation but not every relation is a function. C. If the domain of a function consists of more than one​ element, then the range must also consist of more than one element. D. 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.

C. 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 best defines a relative maximum of a function y=​f(x)? A. 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). 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=c. C. 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. 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).

C. 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.

Which of the following does not describe the​ slope, m, of a nonvertical line passing through the points (x1, y1) and (x2,y2)​? Choose the incorrect description below. A. m= change in y / change in x B. m= y2−y1 / x2-x1 C. m= x2−x1 / y2−y1 D. m= rise/run

C. m= x2−x1 / y2−y1

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

Which of the following statements is​ true? A. The graph of every odd function is symmetric about the​ y-axis. B. The graph of every even function is symmetric about the origin. C. A function y=f(x) is even if for every point (x1, y1) on the graph of​ f, the point (x1, −y1) also lies on the graph of f. D. A function y=f(x) is odd if for every point (x1, y1) on the graph of​ f, the point (−x1, −y1) also lies on the graph of f.

D. A function y=f(x) is odd if for every point (x1, y1) on the graph of​ f, the point (−x1, −y1) also lies on the graph of f.

Which of the following statements is ​true? A. A graph in the Cartesian plane is the graph of a function if every horizontal line intersects the graph no more than once. B. A graph in the Cartesian plane is the graph of a function if every vertical line intersects the graph at least 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 statement describes how to derive the equation of a circle in standard​ form? A. The equation of a circle can be derived using the quadratic formula. B. The equation of a circle can be derived using the midpoint formula. C. The equation of a circle can be derived by solving a quadratic equation using the method of completing the square. D. The equation of a circle can be derived using the distance formula.

D. The equation of a circle can be derived using the distance formula.

Which of the following statements is​ true? A. 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. B. If a rational function has a vertical​ asymptote, then the domain of the function can never be (−∞, ∞). C. The domain of a function must always be the same as the range of a function. 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 (−∞, ∞).

Let line 1 with slope m1 and line 2 with slope m2 be two nonvertical perpendicular lines. Which of the following statements is not ​true? Choose the incorrect statement below. A. The value of m1 does not equal the value of m2. B. It is possible for the value of m1 to be zero. C. If m1= a/b, then m2= -b/a D. The product of m1m2 is equal to −1.

B. It is possible for the value of m1 to be zero.

Given a linear system of {Ax+By=C and Dx+Ey=F} where​ A, B,​ D, and E are nonzero real​ numbers, which of the following statements is not​ true? Choose the incorrect statement below. A. It is possible to multiply one equation of a linear system in two variables by a nonzero constant without changing the solution to the system. B. The method of elimination can only be used when one of the variables in both of the original equations have coefficients with opposite signs. C. Every system of linear equations of this form can be solved using the method of elimination. D. Every system of linear equations of this form can be solved using the method of substitution.

B. The method of elimination can only be used when one of the variables in both of the original equations have coefficients with opposite signs.