Multiple Choice De Advanced Math
The graph of which of the following basic functions is increasing on the interval (−∞, ∞)? (3)
cube root function
The right-hand behavior of the graph of a polynomial function of the form f(x)=anxn+an−1xn−1+an−2xn−2+. . .+a1x+a0 can be determined by... (3)
the sign of the leading coefficient an.
Identify the collection of three functions whose graphs are all symmetric about the origin. (3)
y=1/x, y=x, y=3x (cube root function)
Identify the collection of three functions that are all even. (3)
y=−3, y=x^2, and y=IxI
If u is an algebraic expression and c is a real number such that c>0, then the inequality u<c is equivalent to ... (1)
−c<u<c.
If u is an algebraic expression and c is a real number such that c>0, then the inequality u>c is equivalent to ... (1)
u<−c or u>c.
If u is an algebraic expression and c is a real number such that c>0, then the equation u=c is equivalent to ... (1)
u=−c or u=c.
To what is the expression logbb^x, for b>0 and b≠1, equal? (4)
x
Which of the following does not describe the slope, m, of a nonvertical line passing through the points(x1,y1) and (x2,y2)? (2)
x2−x1 y2−y1
Which of the following equations is not a disguised quadratic equation? (1)
x5−x3−6=0
For x>0, b>0 and b≠1, if y=logb^x, then which of the following is true? (4)
x=b^y
Which of the following basic functions is equivalent to the piecewise-defined function f(x)=x if x≥0 −x if x<0? (3)
. f(x)=IxI
Which of the following statements is not true? (3)
Every function that passes the vertical line test is one-to-one.
Which of the following statements is not true? (3)
If f has an inverse function, then f^−1(x)=1/f(x).
Which of the following statements is not true about the profit business model? (3)
The revenue is always more than the cost.
Which of the following equations is in point-slope form? (2)
. y−y1=m(x−x1)
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? (3)
. The graph of y=f(x)+c can be obtained by vertically shifting the graph of y=f(x) up c units.
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? (1)
. There must be two real solutions.
Which of the following statements is not true? (2)
A function can have several y-intercepts.
Which of the following statements defines a function? (2)
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? (2)
A function is increasing on an interval left parenthesis a comma b right parenthesis (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? (2)
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? (2)
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 about a rational function of the form f(x)=g(x)/h(x) where g and h are polynomial functions? (4)
A rational function may have many horizontal asymptotes.
Which of the following statements defines a relation? (2)
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 about the revenue business model? (3)
A revenue function can never be defined as a function of the price p.
Which of the following statements is not true? (2)
A system of linear equations in two variables must have at least one solution.
Which of the following statements most commonly describes the relationship between the quantity x of a product and the price p? (3)
As the quantity x increases, the price p tends to decrease.
Which of the following statements is true? (1)
All linear equations and all quadratic equations are polynomial equations.
Which of the following statements best defines the term "extraneous solution"? (1)
An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.
Which of the following statements about projectile motion is not true? (3)
An object thrown or shot vertically into the air reaches a maximum height after t seconds (when time is measured in seconds), where t is the k-coordinate of the vertex of the parabola.
Which of the following statements is not true? (2)
It is possible for the distance between two points to be negative.
Which of the following is not a valid strategy when solving a polynomial equation of the form ax3+bx2=cx? (1)
Divide the equation by x.
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? (2)
It is possible for the value of m1 to be zero.
Which of the following is not a property of inequalities? (1)
For c<0, if a<b, a−c>b−c.
Which of the following statements is not true? (2)
Given an ordered pair of the form (x,y), y is called the coordinate.
Which of the following statements is not true? (2)
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? (3)
If 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.
If f and g are inverse functions of one another, then which of the following is not necessarily true? (3)
If f(1)=−b, then g(b)=−1.
Which of the following is not true about the shape of a power function of the form f(x)=ax^n? (3)
If n is odd, the shape of the graph resembles a parabola.
Which of the following statements is not true? (2)
If n≥2 is an odd integer, then the domain of..
Which of the following statements is not true? (2)
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 best describes the zero product property? (1)
If two factors multiplied together are equal to zero, then at least one of the factors must be zero.
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? (4)
In order to correctly determine the vertical asymptotes, it is essential to cancel any common factors of g and h.Which of the following statements is not true about a rational function of the form f left parenthesis x right parenthesis equals StartFraction g left parenthesis x right parenthesis Over h left parenthesis x right parenthesis EndFraction f(x)= g(x) h(x) where g and h are polynomial functions?
Which of the following statements is true about rational equations? (1)
It is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions.
Which of the following statements is true? (1)
It is possible for an absolute value equation to have no solution.
Which of the following statements is not true? (3)
It is possible for a piecewise-defined function to have more than one y-intercept depending on how the function is defined..
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? (3)
One endpoint of the range will always be the value of c.
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? (3)
Reflect the graph of f about the line y=x to obtain the graph of f^−1.
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? (4)
Relating the bases by setting u=v.
For the polynomial function y=f(x) below, choose the statements that most accurately describe the function. (3)
Statements II, IV, and V accurately describe this function.
In the definition of the exponential function f(x)=b^x, what are the stipulation(s) for the base b? (4)
The base b must be greater than zero and not equal to 1. .
Given two points which represent the endpoints of the diameter of a circle, which of the following statements is true? (2)
The center of the circle is the midpoint of the given endpoints of the diameter
Which of the following statements is true about linear equations of the form ax + b =0? (1)
The constants a and b must be real numbers with the constant a never equal to zero.
Which of the following statements is true about the quadratic function ax^2+bx+c? (3)
The constants a, b, and c must be real numbers with a not ever equal to zero.
Which of the following statements describes the absolute value of a number a? (1)
The distance from the number a to 0 on a number line can be represented by the absolute value of a number a.
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? (4)
The domain of f(x) consists of all values of x such that g(x)≠0 and h(x)≠0.
Which statement describes how to derive the equation of a circle in standard form? (2)
The equation of a circle can be derived using the distance formula.
Which of the following statements is true about the equation y=b? (2)
The equation y=b is the equation of a horizontal line with zero slope.
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? (4)
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.
Which of the following statements is not true about the characteristics of the graph of f(x)=ax^2+bx+c? (3)
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.
Which of the following statements is not true for the graph of f(x)=b^x, where 0<b<1? (4)
The graph of f(x)=b^x approaches 0 as x approaches negative infinity.
Which of the following statements is not true for the graph of f(x)=e^x? (4)
The graph of f(x)=e^x lies between the graphs of y=3^x and y=4^x.
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)? (3)
The graph of y=f(x+c) can be obtained by horizontally shifting the graph of y=f(x) to the left c units.
Which of the following statements is not true for the graph of y=logb^x for b>1? (4)
The graph of y=logb^x is decreasing on the interval (0,∞).
Given a linear system of the form Ax+By=C Dx+Ey=F where A, B, D, and E are nonzero real numbers, which of the following statements is not true? (2)
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 about the number e is not true? (4)
The number e is a rational number.
Which of the following statements is not true about the polynomial function f(x)=anxn+an−1xn−1+an−2xn−2+. . .+a1x+a0? (3)
The numbers an, an−1, an−2, . . ., a1, and a0 are positive real numbers.
Which of the following statements is true about a rational function of the form f(x)=g(x)/h(x) where g and h are polynomial functions? (4)
The rational function f(x)=g(x)/h(x) will have a removable discontinuity only if g(x) and h(x) share a common factor.
Given the graph of a quadratic function with the vertex and the y-intercept clearly identified, which of the following statements is not true? (3)
The value of b in f(x)=ax^2+bx+c can easily be determined from the shape of the graph.
Given that the points (x1,y1) and (x2,y2) are endpoints of a line segment, which of the following statements is true? (2)
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 concerning the equation x2−c=0 for c>0? (1)
This equation is not considered to be a quadratic equation because it is not of the form ax2+bx+c=0.
Which of the following is typically not one of the three ways to describe the solutions to a linear inequality? (1)Write the solution in inequality form.
Write the solution in inequality form.
The shape of the graph of a polynomial function near the x-intercepts can be determined by.... (3)
examining the multiplicity of the real zeros.
The domain of f(x)=logb[g(x)] can be determined by finding the solution to which inequality? (4)
g(x)>0