Deck 1: Preparation for Calculus

Question 1

Determine the period and amplitude of the function. ​ ​

A) Amplitude: -3; Period:
B) Amplitude: 3; Period:
C) Amplitude: 3; Period:
D) Amplitude: -3; Period:
E) Amplitude: not applicable; Period:

Answer 1

C

Question 2

You need 50 pounds of two commodities costing $ and $ per pound. Find the inverse function of the cost function . ​

A)
B)
C)
D)
E)

Answer 2

D

Question 3

Find the slope of the line passing through the pair of points. ​ ​

A)
B)
C)
D)
E) 0

Answer 3

B

Question 4

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. ​

A)
B)
C)
D)
E)

Question 5

A company reimburses its sales representatives per day for lodging and meals plus ¢ per mile driven. Write a linear equation giving the daily cost to the company in terms of , the number of miles driven. Round the numerical values in your answer to two decimal places, where applicable. ​

A)
B)
C)
D)
E)

Question 6

Determine two coterminal angles in radian measure (one positive and one negative) for the angle. ​ ​
Where .
​

A)
B)
C)
D)
E)

Question 7

Find an equation of the line that passes through the point (7, -5) and has the slope m that is undefined. ​

A)
B)
C)
D)
E)

Question 8

An open box of maximum volume is to be made from a square piece of material 30 centimeters on a side by cutting equal squares from the corners and turning up the sides(see figure). What is the domain of the function V = x(30 - 2x)². ​ ​

A) domain: 0 < x < ∞
B) domain: 30
C) domain: 0 < x < 15
D) domain: 0 < x < 30
E) domain: 15

Question 9

Find two solutions of the equation. Give your answers in radians ( ). Do not use a calculator. ​ ​

A)
B)
C)
D)
E)

Question 10

True or False: The function is one-to-one on the domain .
​

Question 11

Solve the following equation for x. ​ ​

A)
B)
C)
D)
E) no solution

Question 12

Find the domain of the function . ​

A)
B)
C)
D)
E)

Question 13

Evaluate the expression without using a calculator. ​

A) 0
B)
C)
D)
E)

Question 14

Write an equation of the line that passes through the point and is parallel to the line . ​

A)
B)
C)
D)
E)

Question 15

What is the domain of the function f(x) = 12ln(2x)? ​

A)
B)
C)
D)
E)

Question 16

Find the sales necessary to break even if the cost of producing units is and the revenue R for selling x units is . Round your answer to the nearest integer. ​

A)
B)
C)
D)
E)

Question 17

Sketch the graph of the function. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 18

If a line has slope and passes through the point , through which of the following points does the line also pass? ​

A) (3, 12)
B) (3, 5)
C) (3, -12)
D) (7, -15)
E) (7, -28)

Question 19

Find if . ​

A)
B)
C)
D)
E)

Question 20

You need 50 pounds of two commodities costing $1.55 and $1.90 per pound. Determine the number of pounds of the less expensive commodity purchased if the total cost is . ​

A) 20 pounds
B) 27 pounds
C) 17 pounds
D) 15 pounds
E) 23 pounds

Question 21

Specify a sequence of transformations for the function that will yield the graph of h from the graph of the function f(x) = sinx. ​

A) The function is a horizontal shift unit to the right, followed by a vertical shift 3 units downwards.
B) The function is a horizontal shift unit to the left, followed by a vertical shift 3 units upwards.
C) The function is a horizontal shift unit to the left, followed by a horizontal shift 3 units to the right.
D) The function is a vertical shift unit downwards, followed by a horizontal shift 3 units to the right.
E) The function is a vertical shift unit upwards, followed by a horizontal shift 3 units to the left.

Question 22

Find the domain of the function . ​

A)
B)
C)
D)
E)

Question 23

The horsepower H required to overcome wind drag on a certain automobile is approximated by H(x) = 0.004x² + 0.002x - 0.026, 10 ≤ x ≤ 100, where x is the speed of the car in miles per hour. Find . Round the numerical values in your answer to five decimal places. ​

A)
B)
C)
D)
E)

Question 24

Match the graph of the function given below with the graph of its inverse function. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 25

Find if . ​

A)
B)
C)
D)
E)

Question 26

Given f(x) = cos x and , evaluate f(g(-3)). ​

A) 1
B)
C)
D) 0
E)

Question 27

Write the following expression in algebraic form. ​ ​

A)
B)
C)
D)
E)

Question 28

A moving conveyor is built to rise 1 meter for every 7 meters of horizontal change. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the vertical distance between floors is 10 meters. Round your answer to the nearest meter. ​

A) 81 meters
B) 59 meters
C) 71 meters
D) 70 meters
E) 61 meters

Question 29

Write the exponential equation as a logarithmic equation. ​ ​

A)
B)
C)
D)
E)

Question 30

Find the distance between the point and line using the formula, for the distance between the point and the line . ​

A)
B)
C)
D)

Question 31

Find all intercepts: ​ ​

A) x-intercepts: (8,0), (-4,0); y-intercepts: (0, 8), (0, 4)
B) x-intercept: (32, 0); y-intercepts: (0, 8), (0, 4)
C) x-intercepts: (8, 0), (-4,0); y-intercept: (0, -32)
D) x-intercepts: (8, 0), (-4,0); y-intercepts: (0, -32), (0, 32)
E) x-intercept: (-4, 0); y-intercept: (0, -32)

Question 32

Evaluate (if possible) the function at . Simplify the result. ​

A) 2
B) undefined
C) -1
D) 3
E) 1

Question 33

Solve the following equation for . ​ ​

A)
B)
C)
D)
E)

Question 34

Write the following expression as a logarithm of a single quantity. ​ ​

A)
B)
C)
D)
E)

Question 35

Use the properties of logarithms to expand the logarithmic expression . ​

A)
B)
C)
D)
E)

Question 36

Write an equation of the line that passes through the given point and is perpendicular to the given line. Point Line
​ ​

A)
B)
C)
D)
E)

Question 37

Evaluate the function at f(2). ​

A) f(2) = 3
B) f(2) = 2
C) f(2) = 7
D) f(2) = 5
E) f(2) = 6

Question 38

Solve the following equation for . ​ ​

A)
B)
C)
D)
E)

Question 39

Which of the following is the correct graph of ? ​

A)
B)
C)
D)
E)

Question 40

Find an equation of the line that passes through the points and . ​

A)
B)
C)
D)
E)

Question 41

Determine whether y is a function of x. y - 4x² = 3
​

A) no
B) yes

Question 42

Determine the quadrant in which lies. ​ and ​

A) IV Quadrant
B) II Quadrant
C) I Quadrant
D) III Quadrant

Question 43

Sketch the line passing through the point (4, 3) with the slope . ​

A)
B)
C)
D)
E)

Question 44

Find an equation of the line through the points of intersection of and . ​

A)
B)
C)
D)
E)

Question 45

A real estate office handles an apartment complex with 50 units. When the rent is per month, all 50 units are occupied. However, when the rent is , the average number of occupied units drops to 47. Assume that the relationship between the monthly rent and the demand is linear. Predict the number of units occupied if the rent is raised to . ​

A) 37 units
B) 60 units
C) 63 units
D) 43 units
E) 40 units

Question 46

Determine whether the function is even, odd, or neither. ​
F(x) = x sin2x
​

A) even
B) odd
C) neither

Question 47

Write an equation for the function having the given characteristics: ​
The shape of but shifted nine units to the left and eleven units downward.
​

A)
B)
C)
D)
E)

Question 48

Find the slope of the line passing through the points and . ​

A) 26
B) -5
C)
D) 5
E) -

Question 49

Find all intercepts: ​ ​

A) x-intercepts: (-3, 0), (3, 0); no y-intercept
B) x-intercept: (0, 0); y-intercepts: (0, 0), (0, -3), (0, 3)
C) x-intercepts: (0, 0), (-3, 0), (3, 0); y-intercept: (0, 0)
D) x-intercepts: (0, 0), (-3, 0), (3, 0); no y-intercept
E) x-intercepts: (-3, 0), (3, 0); y-intercept: (0, 0)

Question 50

Write the following expression in algebraic form. ​ ​

A)
B)
C)
D)
E)

Question 51

Find the points of intersection of the graphs of the equations: ​

A)
B)
C)
D)
E)

Question 52

Write an equation of the line that passes through the given point and is parallel to the given line. Point Line
​ ​

A)
B)
C)
D)
E)

Question 53

Determine two coterminal angles in degree measure (one positive and one negative) for the angle. ​ ​

A) 128, -128
B) 412, -412
C) 308, -308
D) 308, -412
E) 412, -308

Question 54

Find an equation of the line that passes through the points and . ​

A)
B)
C)
D)
E)

Question 55

Find the domain and range of the function . ​

A) domain:
Range:
B) domain:
Range:
C) domain:
Range:
D) domain:
Range:
E) none of these

Question 56

Sketch a graph of the equation . ​

A)
B)
C)
D)
E)

Question 57

Solve the equation for , where . ​ ​

A)
B)
C)
D)
E)

Question 58

Test for symmetry with respect to each axis and to the origin. ​

A) symmetric with respect to the origin
B) symmetric with respect to the x-axis
C) symmetric with respect to the y-axis
D) no symmetry
E) symmetric with respect to the origin; symmetric with respect to the x-axis; and symmetric with respect to the y-axis

Question 59

Find the y-intercept of the line . ​

A) (0, 5)
B) (0, 7)
C) (0, 35)
D) (7, 0)
E) (5, 0)

Question 60

What is the domain of the function f(x) = 16 + ln(x - 15)? ​

A)
B)
C)
D)
E)

Question 61

An open box of maximum volume is to be made from a square piece of material 22 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). Write the volume V as a function of x, the length of the corner squares. ​ ​

A) V = x(22 - 2x)²
B) V = x + (22 - 2x)²
C) V = x² + (22 - 2x)
D) V = x²(22 - 2x)
E) V = x(22 - 2x)

Question 62

Use the functions and to find the function . ​

A)
B)
C)
D)
E)

Question 63

Use the graph of y = f(x) given below to find the graph of the function y = f(x) + 4. ​ ​

A)
B)
C)
D)
E)

Question 64

Suppose that the dollar value of a product in and the rate at which the value of the product is expected to increase per year during the next . Write a linear equation that gives the dollar value of the product in terms of the year . (Let represent 2,000.) Round the numerical values in your answer to one decimal place, where applicable. ​

A)
B)
C)
D)
E)

Question 65

Evaluate the expression without using a calculator. ​

A)
B)
C)
D)
E)

Question 66

Evaluate the expression without using a calculator. ​

A)
B)
C)
D)
E)

Question 67

The resistance y in ohms of 1000 feet of solid metal wire at can be approximated by the model , where is the diameter of the wire in mils (0.001 in). If the diameter of the wire is doubled, the resistance is changed by approximately what factor? In determining your answer, you can ignore the constant -0.38. ​

A) 5
B)
C) 4
D)
E)

Question 68

Evaluate (if possible) the function at . Simplify the result. ​

A) 9
B) 31
C) 7
D) 33
E) undefined

Question 69

Solve the following equation for x. ​ ​

A)
B)
C)
D)
E)

Question 70

Find , , and such that the graph of the function matches the graph in the figure. ​ ​ ​

A)
B)
C)
D)
E)

Question 71

Sketch the graph of the equation: ​ ​

A)
B)
C)
D)
E) none of these

Question 72

Solve the equation for , where . ​ ​

A)
B)
C)
D)
E)

Question 73

Test for symmetry with respect to each axis and to the origin. ​ ​

A) symmetric with respect to the origin
B) symmetric with respect to the y-axis
C) symmetric with respect to the x-axis
D) both symmetric with respect to the y-axis and symmetric with respect to the x-axis
E) no symmetry

Question 74

True or False: The function is one-to-one on its entire domain.
​

Question 75

Write the following expression as a logarithm of a single quantity. ​ ​

A)
B)
C)
D)
E)

Question 76

Which of the following is the correct graph of ? ​

A)
B)
C)
D)
E)

Question 77

Sketch the graph of the function. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 78

Which of the following is the correct graph of ? ​

A)
B)
C)
D)
E)

Question 79

Convert the radian measure to degree measure. ​ ​

A)
B)
C)
D)
E)

Question 80

Use the graph of y = f(x) given below to find the graph of the function y = f(x + 1). ​

A)
B)
C)
D)
E)