1021 Chapter 2

D

Which of the following equations does not represent a line perpendicular to the line 8x-4y=1? A. y-4=-1/2(x+8) B. y=-1/2x C. x+2y=7 D. 4x-8y=1

C

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

D

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

D

Which of the following is not a linear equation? A. √7x-3y=0.02 B. 1/2x1-5/8x2-7/16x3=0 C. 2x-9=5 D. 3x+2y-4z^2=2

A

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

B

Which of the following statements is not true? A. An equation of the line through the point (-2,4) and perpendicular to y=3x-5 is x+3y=10. B. The lines y=(3/2x)-7 and 2x-3y=6 are perpendicular C. Given any two distinct non vertical lines in the Cartesian plane, whether the lines are parallel to each other, perpendicular to each other, or neither can be determined by evaluating their slopes. D. If two non vertical lines are perpendicular, then the product of their slopes must be negative one.

B

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

A

Given a linear system of the form 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? A. The method of elimination can only be used when one of the variables in both of the original equations have coefficients with opposite signs. B. Every system of linear equations of this form can be solved using the method of substitution. C. Every system of linear equations of this form can be solved using the method of elimination. D. 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.

D

Given the circle with equation (x+2)^2 + (y-5)^2=4, which of the following statements is not true? A. The center of the circle is (-2,5) B. The radius of this circle is 2. C. This circle has one y-intercept. D. This circle has one x-intercept.

A

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

C

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

B

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

C

Given the circle with equation x^2+y^2-8x +6y+16=0, which of the following statements is true? A. The radius of the circle is 4. B. The radius of the circle is 16. C. The center of this circle is (4,-3). D. The center of this circle is (-4,3).

C

Which of the following does not describe the slope, m, of a non vertical line passing through the points (x1,y1) and (x2,y2)? A. m=change is y/ change in x B. m=y2-y1/ x2-x1 C. m=x2-x1/y2-y1 D. m=rise/ run

B

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

D

Given the circle with the equation (x+2)^2 + )y-5)^2 = 4, which of the following statement is not true? A. The circle has one y-intercept. B. The radius of this circle is 2. C. The center of the circle is (-2, 5). D. The circle has one x-intercept.

C

Given the equation 4x^2 +4y^2+4x-8y+1=0, which of the following statements is not true? A. This equation is said to be the equation of a circle in general form. B. This equation represents a circle with radius to 1. C. This equation does not represent the equation of a circle because the x^2-term and the y^2-term are not equal to one. D. The graph of this equation has two y-intercepts.

B

Given the equation of a line in standard form, Ax+By=C with B≠0, which of the following represents the slope of this line? A. m=-B/A B. m=-A/B C. m=A/B D. m=C/B

B

Given two points which represent the endpoints of the diameter of a circle, which of the following statements is true? A. The center of the circle cannot be found without additional information. B. The center of the circle is the midpoint of the given endpoints of the diameter. C. 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. D. 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.

D

If a system of linear equation is two variables can be represented by two distinct lines having different slopes, then which of the following accurately describes the system? A. The system is said to be an inconsistent, dependent system B. The system is said to be inconstant, independent system C. The system is said to be consistent, dependent system. D. The system is said to be a consistent, independent system.

D

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

B

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

A

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

D

Which of the following statements describes the process of verifying that an ordered pair of the form (b,c) is a solution to a system of two linear equations in two variables?\ A. To verify that the ordered pair (b,c) is a solution, show that b is a solution to the first equation by substituting the value of b in for the first variable and then show that c is a solution to the second equation by substituting the value of c in for the second variable. B. To verify that the ordered pair (b, c) is a solution, show that both b and c are solutions to either equation by substituting the value of b for the first variable in either equation and by substituting the value of c for the second variable in either equation. C. To verify that the ordered pair (b,c) is a solution, show that b is a solution to either equation by substituting the value of b in for the first variable and then show that c is a solution to either equation by substituting the value of c in for the second variable. D. To verify that the ordered pair (b,c) is a solution, show that both b and c are solutions to both equations by substituting the value of b in for the first variable in both equations and by substituting the value of c in for the second variable in both equations.

B

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

C

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. Two or more distinct elements in the domain of a function can correspond to the same element in the range. 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. Every function is a relation but not every relation is a function.

D

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

B

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

C

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 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 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

Which of the following statements is true? A. The domain of a function must always be the same as the range of the function. B. The domain of a function is (-∞,∞), then the function cannot have a horizontal asymptote. C. If a rational function has a vertical asymptote, then the domain of the function can never be (-∞,∞). D. 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

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 midpoint formula. B. The equation of a circle can be derived by solving a quadratic equation using the method of completing the square. C. The equation of a circle can be derived using the quadratic formula. D. The equation of a circle can be derived using the distance formula.