MATH 1021 TEST 3

Which of the following statements about projectile motion is not​ true?

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 most commonly describes the relationship between the quantity x of a product and the price​ p?

As the quantity x​ increases, the price p tends to decrease.

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.

Which of the following statements is true?

When solving a polynomial inequality, choose a test value from an interval to test whether the inequality is positive or negative on that interval.

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.

Identify the collection of three functions that are all even.

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

Identify the collection of three functions whose graphs are all symmetric about the origin.

y=1/x, y=x, and y∛x

When encountering a combination of several transformation, which of the following represents the order suggested in the textbook?

(1) Horizontal shifts (2) Horizontal stretches/compression (3) Reflection about y-axis (4) Vertical stretches/compression (5) reflection about x-axis (6) vertical shifts

Which of the following statements is not true about the revenue business​ model?

A revenue function can never be defined as a function of the price p.

Which of the following statements is not true?

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, solving for x.

Which of the following statements is not true?

If a polynomial inequality of the form p<0 has m distinct boundary points, then the boundary points divide the number line into m distinct intervals.

3 Which of the following statements is not true?

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

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.

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

The constants a, b, and c cannot ever be fractions.

Suppose that the graph of a quadratic function f is a parabola opening down and has a vertex with coordinates (3,-1). Which of the following statements is not true?

The function f(x)=-x^2+6x-8 is a possible quadratic function that describes this parabola.

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.

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.

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.

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

examining the multiplicity of the real zeros.

Suppose f(g(x))=x^2. Which of the following is not a possibility for f and g?

f(x)=x^2-2x-1 and g(x)=x+1

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|

The graph of which of the following basic functions is increasing on the interval (-∞,∞)?

f(x)=∛x

2 Which of the following statements is not true?

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

Given any two functions f and g, which of the following statements is not true?

If x is in the domain of f and if x is in the domain of g, then x must be in the domain of f(g).

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.

In an inequality such as (x+a)(x+b)(x+c)>0, which of the following is not a reason why setting each factor greater than zero and solving for x does not produce all of the solutions?

It is possible that (x+a)<0, (x+b)<0, and (x+c)<0.

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.

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

Reflect the graph of f about the line y=x to obtain the graph of f^-1.

Which of the following is not a valid step in the process of solving the inequality (x+1)(x+2)(x+3)>0?

Set up three inequalities by setting each factor greater than zero and solve for x to determine all of the intervals which satisfy the inequality

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.

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.

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.

Which of the following statements is not true about the profit business​ model?

The revenue is always more than the cost.