A collection of data yields a correlation coefficient of 0.95, indicating which of the following?

	a. The data points have a slope close to 1.
	b. The data points are normally distributed.
	c. The data points are nearly linear.
	d. The data points have very little correlation.

.

Calculate the average rate of change of j(x) = x³ - 5 over the interval [-2, 6].

	a. 0.0202
	b. 0.0357
	c. 28
	d. 48

.

Consider a function f(x) = axⁿ + b, where a, b, and n are integers larger than 1. Which of the following statements is true?

	a. If n is odd, there will be an absolute maximum.
	b. If n is even, there will be an absolute minimum.
	c. There will be neither an absolute maximum nor an absolute minimum.
	d. The existence of extremes cannot be determined without more information.

.

Consider the function and find f[f(2)].

	a. -3
	b. -1
	c. 4
	d. 8

.

Consider the function f(x)=x²-3x-4 and find f(x+3).

	a. f(x+3)=x2+3x+1.
	b. f(x+3)=x2+3x-4.
	c. f(x+3)=x2-3x.
	d. f(x+3)=x2-3x-1.

.

Find the domain of .

	a. x ≠
	b. x ≠ 4
	c. x<
	d.

.

The expression log₃ ⁡7 is equal to:

	a.
	b.
	c.
	d.

.

The line that passes through the points (-7, -6.75), (3, -14.25), and (-2, -10.5), has which of the following characteristics?

	a. Positive slope and positive y-intercept
	b. Positive slope and negative y-intercept
	c. Negative slope and positive y-intercept
	d. Negative slope and negative y-intercept

.

What is the domain and range of the function g(x) = 4x² - 11.5?

	a. The domain and the range are the same: the set of all real numbers.
	b. The domain and the range are the same: [11.5, +∞).
	c. The domain is [-11.5, +∞); the range is all real numbers.
	d. The domain is all real numbers; the range is [-11.5, +∞).

.

Which of the following relations describes a function of x?

	a. y = 3x + 1
	b. y = (3x + 1)2 -11
	c. x = y
	d. All of these

.

Which set identifies some of the places where the rational function is defined?

	a. {2, 4, 6, 8}
	b. {-1, -3, -5, -7}
	c. {-4,-3, -2, -1, 0, 1, 2, 3}
	d. {-2, -, 0, 1, 2}

.

Find the value of x such that m(x) = 3 if m(x) =

	a. -3
	b. -1
	c. 2
	d. 4

.

Find x such that g(x) = 7 : g(x) =

	a. -5
	b. 4
	c. 10
	d. The answer is irrational.

.

Solve (4x - 5)(4x² + 15x - 4) 0.

	a.
	b.
	c. (0.25, 1.25]
	d. [0.25, 1.25]

.

Solve 7^x = 8.

	a.
	b.
	c.
	d.

.

Solve for c: If a = b^c, then c =

	a.
	b.
	c.
	d.

.

Solve for x: 2^x+3 = 3^2x-1.

	a.
	b.
	c.
	d.

.

Solve for x: 2^x+5 = 12.

	a. x = log 6 - 5
	b. x = - 5
	c. x = - 5
	d. x = - 5

.

Solve for x: log₂x = 3 - log₂(x - 2).

	a. x = -2
	b. x = -2 or 4
	c. x = 4
	d. x is undefined

.

Solve the inequality p⁴ - p³ - 20p²< 0.

	a. [-4, 5]
	b. (-4, 5)
	c. (-4, 0) (0, 5)
	d.

.

Solve the inequality .

	a. [1, 3]
	b.
	c. [-2, 3]
	d.

.

Consider a function f(x) = axⁿ + bx, where a , b and n are integers larger than one. Which of the following statements is true?

	a. If n is odd, the ends of the graph both tend in the positive direction.
	b. If n is even, the ends of the graph both tend in the positive direction.
	c. The ends of the graph will both tend in different directions.
	d. The end behavior cannot be determined without more information.

.

Consider the function h(x) = log_bx, where x is a positive real number. Which of the following statements is true?

	a. The point (1, 0) is on h(x).
	b. The right-hand end behavior of h(x) gets large toward positive infinity.
	c. The domain of h(x) is all positive real numbers.
	d. All of these.

.

Given the function g(x), identify a function with a graph two units to the left and five units down.

	a. g(x-5) + 2
	b. g(x) - 3
	c. g(x + 5) - 2
	d. g(x + 2) - 5

.

The graph of an exponential function:

	a. usually has both positive and negative y- values.
	b. contains the point (0, 1).
	c. has a horizontal asymptote at y = 1.
	d. has a domain of positive real numbers.

.

The graph of the function will have a vertical asymptote at:

	a. 2.
	b. 3.
	c. 5.
	d. 8.

.

What kind of function is depicted in the graph?

	a. Polynomial
	b. Piecewise
	c. Odd
	d. Even

.

What kind of function is depicted in the graph?

	a. Exponential
	b. Rational
	c. Quadratic
	d. Cubic

.

What kind of function is depicted in the graph?

	a. Polynomial
	b. Piecewise
	c. Logarithmic
	d. Even

.

Which of the following shows the graph of a logarithmic function?

A. B.
C. D.

	A.
	B.
	C.
	D.

.

Which of the following shows the graph of a rational function?

A. B.
C. D.

	A.
	B.
	C.
	D.

.

Consider m(k) = 4x³ - 7. Find m^-1(k).

	a.
	b.
	c.
	d.

.

Consider the function f(x) = b^x, where b is a positive real number. What is the domain of f^-1(x)?

	a. All real numbers
	b. x > 0
	c. x > b
	d. 0 < x < b

.

Consider the two inverse functions h(x) and h^-1(x). Which of the following is true about graphing the two functions?

	a. The two graphs make a mirror image over the x-axis.
	b. The two graphs make a mirror image over the y-axis.
	c. The two graphs make a mirror image over the line y = x.
	d. The two graphs make a mirror image over the line y = -x.

.

Find the inverse of the function .

	a.
	b.
	c.
	d.

.

If and ,

	a. 1.5 (x + 5).
	b. .5(x + 5).
	c. x3 – 5.
	d. x.

.

Let f(x) = x - 3 and g(x) = . Find g(f(3)).

	a. 0
	b. -0.5
	c. 6
	d. 9

.

Let and . Find .

	a.
	b.
	c.
	d.

.

Use the following three functions to determine (g(h(x))): f(x) = x + 2, g(x) = ln (x-5), h(x) = x-1.

	a.
	b.
	c.
	d.

.

Use the following three functions to determine f(g(h(3))): f(x) = x - 4, g(x) = x², h(x) = 2x.

	a. 2
	b. 4
	c. 10
	d. 32

.

Which of the following is true about a one-to-one function?

	a. It is always increasing or decreasing.
	b. It has an inverse.
	c. It does not have an inverse.
	d. It is its own inverse.

.

A ball is hurled upward from the top of a building. Its height at time t (in seconds) can be described by the function H(t)=-16t²+64t+120. If the maximum height of the ball is 150 feet, how many seconds did it take for the ball to reach its maximum height?

	a. 1 second
	b. 1.5 seconds
	c. 2 seconds
	d. 2.5 seconds

.

A function t(x) has x-intercepts at -4 and 9. Where are the intercepts of t(x - 5)?

	a. At -4 and 9.
	b. At 4 and -9.
	c. At 1 and 14.
	d. At 20 and -45.

.

A polynomial function that has three different roots:

	a. can be inverted only if the domain is restricted.
	b. passes both the vertical and the horizontal line tests
	c. will have no more than two relative maximums.
	d. will have no more than two relative minimums.

.

Find the roots of the function f(x)=4x³+8x²-21x.

	a. 0, 3, 7
	b. 4, 8, -21
	c. 2,
	d. -3.5, -1.5, 0

.

Find the x-intercepts of the function f(x)=3x²-15x-52.

	a. 2 and 7
	b. -2 and 7
	c. -2 and -7
	d. 2 and -7

.

One root of the function g(x)=3x³-12x²-36x:

	a. is at -2, and the function is positive on the left and negative on the right.
	b. is at 0, and the function is negative on the left and positive on the right.
	c. is at 6, and the function is positive on the left and negative on the right.
	d. is at -36, and the function is negative on the left and positive on the right.

.

The following statements refer to the function y=ax²+bx+c. Which statement is true?

	a. The function has a vertex at .
	b. The function has two roots.
	c. The range of the function is all positive real numbers.
	d. The function has one relative maximum.

.

The function f(x)=|x-a|+b has a vertex at which of the following?

	a. (a, b)
	b. (a, -b)
	c. (-a, b)
	d. (-a,-b)

.

The function h(x)=2x-8x-24:

	a. has a minimum at 2.
	b. has a minimum at -2.
	c. has a maximum at 2.
	d. has a maximum at -2.

.

The quadratic function f(x) = -5x² + 30:

	a. has a maximum at -6.
	b. has a minimum at 1.5.
	c. has a minimum at -1.5.
	d. has a maximum at 0.

.

A printer makes reproductions of a series of pictures. They are all different sizes, but each picture has a height that is twice the length of the width. The printer wants to maintain the original proportions but make the area of each reproduction to be half as large as the area of its original picture. Develop a function (R(w)) that would indicate the width of a final reproduction as a function of the width (w) of the original picture.

	a.
	b.
	c.
	d.

.

A radioactive isotope has a half-life of 250 years. How long will it take, approximately, for the substance to be at one third of its original strength?

	a. 160 years
	b. 300 years
	c. 340 years
	d. 400 years

.

A woman throws a stone upward. Its height above the ground at t seconds can be described by h(t) = -16t2 + 48t + 6, where h is in feet. What is the maximum height that the stone can reach?

	a. 32 feet
	b. 42 feet
	c. 48 feet
	d. 56 feet

.

An investment compounded continuously tripled in five years. What was the approximate interest rate?

	a. 11%
	b. 15%
	c. 18%
	d. 22%

.

Newton’s law of cooling indicates the temperature of an object and can be described by the function where S is the surrounding temperature, D is the difference between the initial temperature and the surrounding temperature, t is the time elapsed, and k is the cooling constant. If tea is served at 200 degrees and cools to 150 degrees in 10 minutes, what is the value of the cooling constant?

	a. 0.04465
	b. 0.04532
	c. 0.04687
	d. 0.04796

.

Squares with sides of size x are cut from the four corners of a rectangular piece of cardboard so that the cardboard can be folded into an open-topped rectangular box. The original cardboard is 20 × 24. Which function describes the volume of the resulting box as a function of x?

	a.
	b.
	c.
	d.

.

The cost of producing “doomflots” is $325 for equipment plus another $32 for materials and labor for each one produced. How many “doomflots” need to be produced such that the average cost per “doomflot” is less than $50?

	a. 9
	b. 10
	c. 18
	d. 19

.

The cougar population in Oregon was estimated to be 5,000 animals in 2006, having grown from about 3,150 in 1996. In what year would we expect a population of 7,500?

	a. 2010
	b. 2014
	c. 2018
	d. 2024

.

The Roman Census under Emperor Augustus in 28 BC was listed at 4,063,000. Twenty years later in 8 BC, another census listed the population at 4,233,000. Assuming the figures are accurate, what was the growth rate of Rome in that 20-year period?

	a. 0.77%
	b. 0.78%
	c. 7.7%
	d. 7.8%

.

To the nearest tenth of a year, how long will it take for an investment of $2,000 to double if the interest rate is 3.5% per year, compounded continuously?

	a. 17.6
	b. 18.4
	c. 19.8
	d. 20.2

.

A city engineer is trying to model the shape of a hill using a quadratic function. She places a grid over a photograph of the hill and finds the following points to describe the relation: (-1, -11), (-2, -11), and (0, -9). Which of the following will help the engineer find that function?

	a.
	b.
	c.
	d.

.

Find a function to model the area of a rectangle as shown in the diagram. The point (x,y) is on the line .

	a.
	b.
	c.
	d.

.

Find an equation for a parabola that contains the points (-1, -11) and (3, -11) and contains an absolute maximum of -3.

	a.
	b.
	c.
	d.

.

Find the function that fits the given points:

	a.
	b.
	c.

.

Find the missing table values for

	a. -3, 3, 1, 2, 2
	b. -3, -3, -1, 2, -2
	c. 3, -3, -1, -2, 2
	d. 3, 3, 1, -2, -2

.

Find the missing table values for

	a. -8, 0, 8
	b. -, 0,
	c. -8, 1,
	d. -, 1, 8

.

Find the missing table values for .

	a. -1, 2, 4
	b. undefined, 0, 1
	c. undefined, 1, 2
	d. 0.25, 2, 1

.

If the average rate of change of a function between x = -2 and x = 5 is -7, then:

	a. the function increases between -2 and 5.
	b. the function decreases between -2 and 5.
	c. the function passes from above the axis to below the axis.
	d. the function passes from below the axis to above the axis.

.

Two integers have a sum of 82 and a product of 1,680. Find an equation to model the relation.

	a.
	b.
	c.
	d.

.

Which function is most likely associated with the following graph?

	a.
	b.
	c.
	d.

.

A fly lights on the edge of an 18 ×12-inch picture frame and is x units away from a bottom corner, as designated by the star on the diagram. Which function describes how far the fly is from the top left corner?

	a.
	b.
	c.
	d.

.

A gardener has 200 feet of fencing to use to enclose an area for a rectangular garden. By putting the garden against one wall of the house, only three sides need to be fenced. What is a function that would describe the area of the resulting garden space if x is the length of the side perpendicular to the wall of the house?

	a. A(x)=200x-2x2
	b. A(x)=x(200-x)
	c. A(x)=2x2-200x
	d. A(x)=2x(200x)

.

A party planner charges $200 plus $7.50 per person for parties up to 20 people. For groups larger than 20, the charge is $17 per person. For groups of more than 50, the party planner charges $16 for each additional person. Which piecewise function describes the cost of the party as a function of the number of people attending?

	a.
	b.
	c.
	d.

.

A portion of fencing 100 feet long is cut into two pieces. One piece, which is x feet long, is used to enclose a square pen. The other piece is shaped into an enclosure as an equilateral triangle. What is the total area enclosed as a function of x?

	a.
	b.
	c.
	d.

.

A rectangle has a perimeter of 36. Find a function A(w) to describe the area of the rectangle, based upon the width.

	a.
	b.
	c.
	d.

.

A square park has 20-foot sides. It is surrounded by a sidewalk that is x feet wide. Which function describes the area of the sidewalk?

	a.
	b.
	c.
	d.

.

A window is made up of a rectangle surmounted by a half circle. The height of the rectangle is 2.4 times the width. Determine a function A(w) to describe the area of the window as a function of the width, w.

	a.
	b.
	c.
	d.

.

The population of rabbits on a farm grows exponentially. If there are currently 245 rabbits and the growth rate is 23%, find a function to describe the number of rabbits after t years.

	a.
	b.
	c.
	d.

.

The volume of a cylinder can be described by the function . Find a formula to describe the volume of a cylinder where the radius is three times the height.

	a.
	b.
	c.
	d.

.

Which of the following functions describes the total amount of money available after investing $5,000 at a rate of 2.3% for t years, compounded continuously?

	a.
	b.
	c.
	d.

.