chapter 2 questions precalc

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 by solving a quadratic equation using the method of completing the square. C. The equation of a circle can be derived using the midpoint formula. 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 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. Your answer is correct.D. Another name for an​ x-intercept is a real zero.

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

Which of the following statements is not​ true?A. The Pythagorean theorem is used to derive the distance formula. B. For any real numbers x 1x1 and x 2x2​, the expression StartAbsoluteValue x 2 minus x 1 EndAbsoluteValue squaredx2−x12 is equivalent to the expression left parenthesis x 2 minus x 1 right parenthesis squared(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 left parenthesis x 1 comma y 1 right parenthesis(x1,y1) and left parenthesis x 2 comma y 2 right parenthesis(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 sum of x 2x2 and x 1x1 and then dividing the sum by two. Your answer is correct.B. The x​-coordinate of the midpoint of the line segment can be found by first taking the difference between x 2x2 and x 1x1 and then dividing the difference by two. C. The x​-coordinate of the midpoint of the line segment can be found by taking the difference between x 2x2 and x 1x1. D. The x​-coordinate of the midpoint of the line segment can be found by taking the sum of x 2x2 and x 1x1.

A. The x​-coordinate of the midpoint of the line segment can be found by first taking the sum of x 2x2 and x 1x1 and then dividing the sum by two.

Which of the following statements best defines a relative maximum of a function yequals=​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 xequals=c. This is the correct answer.B. When a function changes from increasing to decreasing at a point​ (c, f(c)), then f is said to have a relative maximum at xequals=​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 xequals=​f(c). D. When a function changes from decreasing to increasing at a point​ (c, f(c)), then f is said to have a relative maximum at xequals=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 xequals=c.

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

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

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. Your answer is correct.C. If two distinct nonvertical lines are​ parallel, then the two lines must have the same slope. D. Given any two distinct lines in the Cartesian​ plane, the two lines will either intersect or they will be parallel.

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

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 left parenthesis negative infinity comma infinity right parenthesis .(−∞, ∞). This is the correct answer.C. If the domain of a function is left parenthesis negative infinity comma infinity right parenthesis comma(−∞, ∞), then the function cannot have a horizontal asymptote. Your answer is not correct.D. If the domain of a function is the interval left parenthesis a comma b right bracket(a, b] for real numbers a less than b commaa<b, then the line x equals ax=a must be a vertical asymptote.

B. If a rational function has a vertical​ asymptote, then the domain of the function can never be left parenthesis negative infinity comma infinity right parenthesis .(−∞, ∞).

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

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

Which of the following equations is in​ point-slope form? A. y equals mx plus by=mx+b B. y minus y 1 equals m left parenthesis x minus x 1 right parenthesisy−y1=m(x−x1) Your answer is correct.C. Ax plus By equals Upper CAx+By=C D. m equals StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFractionm= x2−x1 y2−y1

B. y minus y 1 equals m left parenthesis x minus x 1 right parenthesisy−y1=m(x−x1)

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. Your answer is correct.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 decreasing on an interval left parenthesis a comma b right parenthesis(a,b) ​if, for any x 1x1 and x 2x2 chosen from the interval with x 1 less than x 2 commax1< x2, then f left parenthesis x 1 right parenthesis less than f left parenthesis x 2 right parenthesis .f(x1)< f(x2). B. A function is decreasing on an interval left parenthesis a comma b right parenthesis(a,b) ​if, for any x 1x1 and x 2x2 chosen from the interval with x 1 greater than x 2 commax1> x2, then f left parenthesis x 1 right parenthesis greater than f left parenthesis x 2 right parenthesis .f(x1)> f(x2). C. A function is increasing on an interval left parenthesis a comma b right parenthesis(a,b) ​if, for any x 1x1 and x 2x2 chosen from the interval with x 1 less than x 2 commax1< x2, then f left parenthesis x 1 right parenthesis less than f left parenthesis x 2 right parenthesis .f(x1)< f(x2). Your answer is correct.D. A function is increasing on an interval left parenthesis a comma b right parenthesis(a,b) ​if, for any x 1x1 and x 2x2 chosen from the interval with x 1 greater than x 2 commax1> x2, then f left parenthesis x 1 right parenthesis less than f left parenthesis x 2 right parenthesis .f(x1)< f(x2).

C. A function is increasing on an interval left parenthesis a comma b right parenthesis(a,b) ​if, for any x 1x1 and x 2x2 chosen from the interval with x 1 less than x 2 commax1< x2, then f left parenthesis x 1 right parenthesis less than f left parenthesis x 2 right parenthesis .f(x1)< f(x2).

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. Your answer is correct.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.

Given a linear system of the form left brace Start 2 By 1 Matrix 1st Row 1st Column Ax plus By equals Upper C 2nd Row 1st Column Dx plus Ey equals Upper F EndMatrix Ax+By=C Dx+Ey=F where​ A, B,​ D, and E are nonzero real​ numbers, which of the following statements is not​ true? 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. Every system of linear equations of this form can be solved using the method of elimination. C. The method of elimination can only be used when one of the variables in both of the original equations have coefficients with opposite signs. Your answer is correct.D. Every system of linear equations of this form can be solved using the method of substitution.

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

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. The graph of a horizontal line in the Cartesian plane cannot represent a function. C. A graph in the Cartesian plane is the graph of a function if every horizontal 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.

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 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 and range of a relation are sets of real​ numbers, then the relation can be represented by plotting ordered pairs in the Cartesian plane. D. 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 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 is true about the equation y equals by=b​? A. The equation y equals by=b is the equation of a horizontal line with zero slope. Your answer is correct.B. The equation y equals by=b is the equation of a vertical line with zero slope. C. The equation y equals by=b is the equation of a vertical line with undefined slope. D. The equation y equals by=b is the equation of a horizontal line with undefined slope.

A. The equation y equals by=b is the equation of a horizontal line with zero slope.

For a number a to be in the domain of a function yequals=​f(x), ​__________ A. ​f(a) must be an integer. B. ​f(a) must be a number greater than or equal to 0. C. ​f(a) must be defined. Your answer is correct.D. ​f(a) must be a rational number.

C. ​f(a) must be defined.

Let line 1 with slope m 1m1 and line 2 with slope m 2m2 be two nonvertical perpendicular lines. Which of the following statements is not ​true? A. It is possible for the value of m 1m1 to be zero. Your answer is correct.B. The product m 1 m 2m1m2 is equal to negative 1−1. C. The value of m 1m1 does not equal the value of m 2m2. D. If m 1 equals StartFraction a Over b EndFractionm1= a b​, then m 2 equals negative StartFraction b Over a EndFractionm2=− b a.

A. It is possible for the value of m 1m1 to be zero.

Which of the following statements is​ true? A. A function y equals f left parenthesis x right parenthesisy=f(x) is odd if for every point left parenthesis x 1 comma y 1 right parenthesis(x1, y1) on the graph of​ f, the point left parenthesis negative x 1 comma negative y 1 right parenthesis(−x1,−y1) also lies on the graph of f. Your answer is correct.B. A function y equals f left parenthesis x right parenthesisy=f(x) is even if for every point left parenthesis x 1 comma y 1 right parenthesis(x1, y1) on the graph of​ f, the point left parenthesis x 1 comma negative y 1 right parenthesis(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 even function is symmetric about the origin.

A. A function y equals f left parenthesis x right parenthesisy=f(x) is odd if for every point left parenthesis x 1 comma y 1 right parenthesis(x1, y1) on the graph of​ f, the point left parenthesis negative x 1 comma negative y 1 right parenthesis(−x1,−y1) also lies on the graph of f.

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

Given the equation of a line in standard​ form, Ax plus By equals Upper CAx+By=C with Bnot equals≠​0, which of the following represents the slope of this​ line? A. m equals StartFraction Upper C Over Upper B EndFractionm= C B B. m equals negative StartFraction Upper A Over Upper B EndFractionm=− A B Your answer is correct.C. m equals negative StartFraction Upper B Over Upper A EndFractionm=− B A D. m equals StartFraction Upper A Over Upper B EndFractionm= A B

B. m equals negative StartFraction Upper A Over Upper B EndFractionm=− A B

Which of the following statements is not ​true? . If n greater than or equals 2n≥2 is an odd​ integer, then the domain of f left parenthesis x right parenthesis equals RootIndex n StartRoot g left parenthesis x right parenthesis EndRootf(x)=ng(x) is the solution to the inequality g left parenthesis x right parenthesis greater than or equals 0.g(x)≥0. Your answer is correct.B. If n greater than or equals 2n≥2 is an even​ integer, then the domain of f left parenthesis x right parenthesis equals RootIndex n StartRoot g left parenthesis x right parenthesis EndRootf(x)=ng(x) is the solution to the inequality g left parenthesis x right parenthesis greater than or equals 0.g(x)≥0. C. Many functions have restricted domains. D. The domain of every polynomial function is all real numbers.

A. If n greater than or equals 2n≥2 is an odd​ integer, then the domain of f left parenthesis x right parenthesis equals RootIndex n StartRoot g left parenthesis x right parenthesis EndRootf(x)=ng(x) is the solution to the inequality g left parenthesis x right parenthesis greater than or equals 0.g(x)≥0.