Math 1021 Multiple Choice

U1: Which of the following statements is​ true?

All linear equations and all quadratic equations are polynomial equations

U1: Which of the following statements best defines the term​ "extraneous solution"?

An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation

U4 5.4: In solving an exponential​ equation, which of the following is not a sound technique to​ use?

If the exponential equation has the form ab^x=c, first "take the log of both sides" and then "bring down any exponents".

U1: Which of the following best describes the zero product​ property?

If two factors multiplied together are equal to​ zero, then at least one of the factors must be zero

U2: Which statement describes how to derive the equation of a circle in standard​ form?

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

U4 5.3: Which of the following is not​ true?

ln x+ln 2x=ln 3x

U1: Which of the following equations is not a disguised quadratic​ equation?

x^5−x^3−6=0

U2: Which of the following equations is in​ point-slope form?

y - y1 = m ( x - x1 )

U1: If u is an algebraic expression and c is a real number such that c>0, then the equation |u|<c is equivalent to

-c<u<c.

U1: Which of the following is a rational​ equation?

6/x -1=4/(x-2)

U2 3.2: Which of the following statements is not ​true?

A function can have several​ y-intercepts.

U2: Which of the following statements defines a​ function?

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

U2 3.2: Which of the following statements is​ true?

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).

U2 3.2: Which of the following statements is​ true?

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.

U2 3.1: Which of the following statements is ​true?

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

U4 4.6: Which of the following statements is not true about a rational function of the form f(x)= g(x)/h(x) where g and h are polynomial​ functions?

A rational function may have many horizontal asymptotes.

U2: Which of the following statements defines a​ relation?

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.

U2: Which of the following statements is not​ true?

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

U4 5.4: In solving the logarithmic equation of the form logb (x+a) +logb (x+c)=d, why is it essential to check the solution(s) to the resulting quadratic equation for potential extraneous solutions to the original logarithmic equation?

All solutions must satisfy x+a>0 and x+c>0.

U4 5.2: To what is the expression logb b^x, for b>0 and b≠1, equal?

x

U4 5.2: For x>0, b>0 and b≠1, if y=logb x, then which of the following is true?

x=b^y

U3 3.3: Identify the collection of three functions whose graphs are all symmetric about the origin

y= 1/x​, y=x​, and y=∛x

U3 3.3: Identify the collection of three functions that are all even.

y=-3, y=x^2, and y=|x|

U1: Which of the following is not a valid strategy when solving a polynomial equation of the form ax^3+bx^2=cx?

Divide the equation by x

U3 3.6: Which of the following statements is not ​true?

Every function that passes the vertical line test is​ one-to-one.

U1: Which of the following is not a property of​ inequalities?

For c<0​, a<b​, a−c>b−c.

U2: Which of the following statements is not ​true?

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

U2: Which of the following statements is not ​true?

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

U3 3.6: Which of the following statements is not ​true?

If f has an inverse function, then f^-1(x)=1/f(x).

U3 3.6: If f and g are inverse functions of one​ another, then which of the following is not necessarily ​true?

If f(1)=-b, then g(b)=-1

U3 4.3: Which of the following is not true about the shape of a power function of the form f(x)=ax^n

If n is​ odd, the shape of the graph resembles a parabola.

U2 3.1: Which of the following statements is not ​true?

If n≥2 is an odd​ integer, then the domain f(x)=n[(root)g(x)] is the solution to the inequality g(x)≥0

U2 3.1: Which of the following statements is not ​true?

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

U4 4.6: Which of the following statements is true about vertical asymptotes of a rational function of the form f(x)= g(x)/h(x) where g and h are polynomial​ functions?

In order to correctly determine the vertical asymptotes, it is essential to cancel any common factors of g and h.

U1: Which of the following statements is true about rational​ equations?

It is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions.

U1: Which of the following statements is​ true?

It is possible for an absolute value equation to have no solution.

U3 3.3: Which of the following statements is not ​true?

It is possible for a​ piecewise-defined function to have more than one​ y-intercept depending on how the function is defined.

U2: Which of the following statements is not​ true?

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

U2: 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?

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

U4 5.3: Why is the logarithmic property of equality, which says that "if logb u=logb v, then u=v" true?

It is true because the logarithmic function is one-to-one.

U3 4.1: For a quadratic function f(x)=ax^2+bx+c, what is not true about the​ domain, the​ range, and the intercepts of the​ function?

One endpoint of the range will always be the h-coordinate of the vertex.

U3 3.6: Given the graph of a​ one-to-one function​ f, which of the following statements best describes how to sketch the graph of f^−1​?

Reflect the graph of f about the line y=x to obtain the graph of f^−1​

U4 5.1 a: If an exponential equation can be written in the form b^u=b^v, then which of the following methods may be used to solve the equation?

Relating the bases by setting u=v.

U4 5.4: In solving the equation ln (x-1)=2, what is the first step?

Rewrite as an exponential equation.

U3 4.3: For the polynomial function y=​f(x) ​below, choose the statements that most accurately describe the function.

Statements​ II, IV, and V accurately describe this function.

5.1 a: In the definition of the exponential function f(x)=b^x, what are the stipulations(s) for the base b?

The base b must be greater than zero but not equal to 1.

U2: Given two points which represent the endpoints of the diameter of a​ circle, which of the following statements is​ true?

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

U1: Which of the following statements is true about linear equations of the form ax plus b equals 0 question mark ax+b=0?

The constants a and b must be real numbers with the constant a never equal to zero.

U3 4.1: Which of the following statements is true about the quadratic function f(x)=ax^2+bx+c

The constants a, b, and c must be real numbers with a not ever equal to zero.

U1: Which of the following statements describes the absolute value of a number a​?

The distance from the number a to 0 on a number line can be represented by the absolute value of a number a.

U4 4.6: Which of the following statements is not true about a rational function of the form f(x)= g(x)/h(x) where g and h are polynomial​ functions?

The domain of f(x) consists of all values of x such that g(x)≠0 and h(x)≠0.

U2: Which of the following statements is true about the equation y=b​?

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

U4 4.6: Which of the following statements is true about horizontal asymptotes of a rational function of the form f(x)= g(x)/h(x) where g and h are polynomial​ functions?

The function f(x)=g(x)/h(x) will have a horizontal asymptote only if the degree of g is less than or equal to the degree of h.

U3 4.1: Which of the following statements is not true about the characteristics of the graph of f(x)=ax^2+bx+c

The graph of f(x)=ax^2+bx+c can have either no x-intercepts or two x-intercepts but never just one x-intercept.

U4 5.1 a: Which of the following statements is not true for the graph f(x)=b^x, where 0<b<1?

The graph of f(x)=b^x approaches 0 as x approaches negative infinity.

U4 5.1 a: Which of the following statements is not true for the graph of f(x)=e^x?

The graph of f(x)=e^x lies between the graphs of y=3^x and y=4^x.

U3 3.4: Given the graph of y=f(x)​, if c is a positive real​ number, then which of the following statements best describes how to sketch the graph of y= f(x) + c

The graph of y=f(x)+c can be obtained by vertically shifting the graph of y=f(x) up c units.

U3 3.4: Given the graph of y=f(x), if c is a positive real number, then which of the following statements best describes how to sketch the graph of y=f(x+c)?

The graph of y=f(x+c) can be obtained by horizontally shifting the graph of y=f(x) to the left c units.

U4 5.2: Which of the following statements is not true for the graph of y=logb x for b>1?

The graph of y=logb x is decreasing on the interval (0,∞).

U2: 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?

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

U4 5.1 a: Which of the following statements about the number e is not true?

The number e is a rational number.

U3 4.3: Which of the following statements is not true about the polynomial function f(x)=AnX^n+A(n-1)X^(n-1)+A(n-2)X^(n-2)+...+A1X+A0?

The numbers an, an-1, an-2,..., a1, and a0, are positive real numbers.

U3 4.1: Given the graph of a quadratic function with the vertex and the​ y-intercept clearly​ identified, which of the following statements is not ​true?

The value of b in f(x)=ax^2+bx+c can easily be determined from the shape of the graph.

U2: Given that the points (x1 , y1) and (x2 , y2) are endpoints of a line​ segment, which of the following statements is​ true?

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.

U1: Suppose that you are solving a quadratic equation and realize that the discriminant is equal to 7. Which of the following statements best describes the solutions to this quadratic​ equation?

There must be two real solutions

U1: Which of the following statements is not true concerning the equation x squared minus c equals 0 for c greater than 0 question mark x^2−c=0 for c>0?

This equation is not considered to be a quadratic equation because it is not of the form of ax^2+bx+c=0.

U4 5.4: Logarithms are studied for which of the following​ reasons?

To help in solving exponential equations when relating the bases cannot be used.

U1: Which of the following is typically not one of the three ways to describe the solutions to a linear​ inequality?

Write the solution in inequality form.

U3 4.3: The shape of the graph of a polynomial function near the x​-intercepts can be determined by

examining the multiplicity of the real zeros.

U3 3.6: Which of the following statements is not ​true?

f a function f has an inverse​ function, then we can find the inverse function by replacing​ f(x) with​ y, interchanging the variables x and​ y, and solving for x.

U3 3.3: The graph of which of the following basic functions is increasing on the interval (−∞, ∞)?

f(x)= ∛x

U3 3.3: Which of the following basic functions is equivalent to the piece-wise-defined function f(x){ x if x≥0 -x if x<0 ?

f(x)=|x|

U4 5.2: The domain of f(x)=logb[g(x)] can be determined by finding the solution to which inequality?

g(x)>0

U4 5.3: Which of the following is​ true?

ln e^8=8

U4 5.3: If a and b are positive real numbers such that a≠1, b≠1, and u is any positive real number then the logarithmic expression logb u is equivalent to which of the following?

loga u/loga b

U4 5.3: If b>0, b≠1, u and v represent positive numbers, and r is any real number, which of the following statements is not a property of logarithms?

logb(u+v)=logb u+logb v

U2: Which of the following does not describe the​ slope, m, of a nonvertical line passing through the points ( x1 , y1 ) and ( x2 , y2 )?

m= x2 - x1 -------- y2 - y1

U3 4.3: The right-hand behavior of the graph of the polynomial function of the form f(x)=AnX^n+A(n-1)X^(n-1)+A(n-2)X^(n-2)+...+A1X+A0 can be determined by

the sign of the leading coefficient an.

U1: If u is an algebraic expression and c is a real number such that c>0, then the equation |u|>c is equivalent to

u<-c or u>c.

U1: If u is an algebraic expression and c is a real number such that c>0, then the equation |u|=c is equivalent to

u=-c or u=c.