test 3 word problems
A
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? A. Reflect the graph of f about the line y=x to obtain the graph of f^−1. B. Reflect the graph about the vertical line x=a for any value of a such that a=f^−1(b). C. First reflect the graph of f about the x-axis, and then reflect the graph about the y-axis to obtain the graph of f^−1. D. Rotate the graph of f ninety degrees counterclockwise to obtain the graph of f^-1.
D
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)? A. The graph of y=f(x+c) can be obtained by vertically shifting the graph of y=f(x) down c units. B. The graph of y=f(x+c) can be obtained by horizontally shifting the graph of y=f(x) to the right c units. C. The graph of y equals f left parenthesis x plus c right parenthesis y=f(x+c) can be obtained by vertically shifting the graph of y=f(x) up c units. D. The graph of y=f(x+c) can be obtained by horizontally shifting the graph of y=f(x) to the left c units.
C
Which of the following statements is not true? A. To verify that two one-to-one functions, f and g, are inverses of each other, we must show that f(g(x))=g(f(x))=x. B. The function f^−1 exists if and only if the function f is one-to-one. C. 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. D. The graph of f^−1 is a reflection of the graph of f about the line y=x.
C
Which of the following statements is true about the quadratic function f(x)=ax2+bx+c? A. The constants a, b, and c must be real numbers with a always positive. B. The constants a, b, and c cannot ever be fractions. C. The constants a, b, and c must be real numbers with a not ever equal to zero. D. The constant c determines whether the graph opens up or down.
A
Identify the collection of three functions that are all even. A. y=−3, y= x^2, and y= |x| B. y= |x|, y= √x, and y= 2 C. y= x, y=x^2, and y=√x D. y= x^2, y= 3, and y= 1/x
D
The graph of which of the following basic functions is increasing on the interval left parenthesis negative infinity comma infinity right parenthesis question mark (−∞, ∞)? A. f(x)= 1/x B. f(x)= x^2 C. f(x)= |x| D. f(x)= 3√
A
Which of the following basic functions is equivalent to the piecewise-defined function f(x)= {x if x>_0 , -x if x<0 ? A. f(x)= |x| B. f(x)=x C. f(x)= 1/x D. f(x)=x^2
A
According to the video, what is the reason why we have been studying one-to-one functions so far in this section? A. Because every one-to-one function has an inverse function B. Because every one-to-one function is a piece-wise defined function C. Because every one-to-one function has an infinite range D. Because every one-to-one function has a finite domain
C
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 A. the sign of the constant coefficient a 0a0. B. the number of terms in the polynomial function. C. the sign of the leading coefficient a Subscript nan. D. the degree n of the polynomial function.
D
Which of the following statements is not true? A. A function f is one-to-one if for any values a not equals ba≠b in the domain of f, f(a)≠f(b). B. A function f is one-to-one if for any two range values f(u) and f(v), f(u)=f(v) implies that u=v. C. Every function that passes the horizontal line test is one-to-one. D. Every function that passes the vertical line test is one-to-one.
B
Which of the following statements is not true? A. Every one-to-one function has an inverse function. B. If f has an inverse function, then f^−1(x)= 1/f(x) C. If f and f^−1 are inverse functions, then the domain of f is the same as the range of f^−1. D. If f and f^−1 are inverse functions and f(a)=b, then f^−1(b)=a.
B
Which of the following statements is not true about the characteristics of the graph of f(x)=ax2+bx+c? A. The graph of f(x)=ax2+bx+c can never have more than one y-intercept. B. The graph of f(x)=ax2+bx+c can have either no x-intercepts or two x-intercepts but never just one x-intercept. C. Since the standard form of the quadratic function is f(x)=a(x−h)2+k, the vertex is always found at the point (h,k). D. The axis of symmetry has the form x=h where h is the x-coordinate of the vertex.
B
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? A. The graph of y=f(x)+c can be obtained by vertically shifting the graph of y=f(x) down c units. B. The graph of y=f(x)+c can be obtained by vertically shifting the graph of y=f(x) up c units. C. The graph of y=f(x)+c can be obtained by horizontally shifting the graph of y=f(x) to the right c units. D. The graph of y=f(x)+c can be obtained by horizontally shifting the graph of y=f(x) to the left c units.
B
Identify the collection of three functions whose graphs are all symmetric about the origin. A. y= x^3, y=x^2, and y=√x B. y= 1/x, y= x, and y= 3√x C. y= x^3, y= 3, and y= 1/x D. y= |x|, y= 1/x, and y= x^3
B
Which of the following statements is not true about the profit business model? A. If a product costs $A to produce and has fixed costs of $B, then the cost function can be represented by C(x)=Ax+B. B. The revenue is always more than the cost. C. The profit function can be represented by P(x)=R(x)−C(x). D. Ideally, the cost will be less than the revenue.
A
Which of the following is not true about the shape of a power function of the form f left parenthesis x right parenthesis equals ax Superscript nf(x)=axn? A. If n is odd, the shape of the graph resembles a parabola. B. If n equals 1n=1, the graph is a straight line. C. If a is positive and n is even, the graph approaches positive infinity on the left side and positive infinity on the right side. D. If a is positive and n is odd, the graph approaches negative infinity on the left side and positive infinity on the right side.
B
Which of the following statements is not true about the revenue business model? A. The revenue function can be represented by R(x)=xp, where x is the quantity sold and p is the price. B. A revenue function can never be defined as a function of the price p. C. Ideally, the graph of a simple revenue function should have a maximum value. D. When the demand equation is linear, it can represented by p=mx+b, where x is the quantity sold and p is the price.
D
If f and g are inverse functions of one another, then which of the following is not necessarily true? A. (f◦g)(x)=x B. (g◦f)(x)=x C. If f(−a)=b, then g(b)=−a. D. If f(1)=−b, then g(b)=−1.
C
The shape of the graph of a polynomial function near the x-intercepts can be determined by A. examining whether the x-intercepts are positive or negative. B. examining the sign of the real zeros. C. examining the multiplicity of the real zeros. D. examining whether the x-intercepts are even or odd.
C
Which of the following statements is not true about the polynomial function f(x)=anxn+an−1xn−1+an−2xn−2+. . .+a1x+a0? A. The number a 0a0 is called the constant coefficient. B. The number a Subscript nan is called the leading coefficient. C. The numbers an, an-1, an−2, . . ., a 1a1, and a 0a0 are positive real numbers. D. The number n represents the degree of the polynomial and is a non-negative integer.
B
Which of the following statements is not true? A. Given the graph of a piecewise-defined function, it is sometimes possible to find a rule that describes the graph. B. It is possible for a piecewise-defined function to have more than one y-intercept depending on how the function is defined. C. The domain of a piecewise-defined function can be left parenthesis negative infinity comma infinity right parenthesis(−∞, ∞). D. The range of a piecewise-defined function can be left parenthesis negative infinity comma infinity right parenthesis(−∞, ∞).
B
Given the graph of a quadratic function with the vertex and the y-intercept clearly identified, which of the following statements is not true? A. The value of c in f(x)=ax2+bx+c can easily be determined because it represents the y-intercept of the graph. B. The value of b in f(x)=ax2+bx+c can easily be determined from the shape of the graph. C. The values of h and k in f(x)=a(x−h)2+k can easily be determined because these values represent the x and y coordinates of the vertex respectively. D. The sign of the value of a in f(x)=ax2+bx+c, or equivalently f(x)=a(x−h)2+k, can easily be determined from the shape of the graph.
A
Which of the following statements about projectile motion is not true? A. 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. B. The acceleration of gravity on earth is approximately 32 feet per second per second. C. 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 h-coordinate of the vertex of the parabola. D. The acceleration of gravity on earth is approximately 9.8 meters per second per second.
A
Which of the following statements most commonly describes the relationship between the quantity x of a product and the price p? A. As the quantity x increases, the price p tends to decrease. B. As the quantity x decreases, the price p tends to stay constant. C. As the quantity x decreases, the price p tends to decrease. D. As the quantity x increases, the price p tends to increase.
