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Questions and Answers
1.
What is the range of a linear function with a negative slope?
A.
R = {y € R | y = –1}
B.
R = {y € R | y < 0 }
C.
R = {y € R }
D.
R = {y € R | y ≠ 0}
Correct Answer C. R = {y € R }
Explanation A linear function with a negative slope will have a range that includes all real numbers. This is because as the x-values increase, the y-values will decrease. Therefore, the function will be able to take on any value from negative infinity to positive infinity.
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2.
What are the domain and range of the function h(x) = x^{2} + 3?
A.
D = {x € R}, R = {y € R }
B.
D = {x € R | 0
C.
D = {x € R, x => 3}, R = {y € R }
D.
D = {x € R}, R = {y € R | y => 3 }
Correct Answer D. D = {x € R}, R = {y € R | y => 3 }
Explanation The domain of the function h(x) = x^2 + 3 is D = {x € R}, which means that the domain includes all real numbers. This is because there are no restrictions or limitations on the values that x can take in order to evaluate the function.
The range of the function is R = {y € R | y >= 3}. This means that the range includes all real numbers y such that y is greater than or equal to 3. This is because the function h(x) = x^2 + 3 will always produce a value that is 3 or greater, regardless of the value of x.
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3.
A crow drops a stick from the air onto the ground. The height of the stick above the ground after it has been release is modeled by the function h(t) = 45 – 5t^{2}, where h(t) is the height in meters and t is time in seconds. What is the domain of the function?
A.
D = {t € R | 0
B.
D = {t = 3}
C.
D = {t € R | 0
D.
D = {t € R | t < 3}
Correct Answer A. D = {t € R | 0
Explanation The domain of the function is {t ∈ R | 0 ≤ t}. This means that the time t can be any real number greater than or equal to zero. Since the function represents the height of the stick above the ground, it makes sense for time to start at zero and continue indefinitely.
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4.
A cable company charges $116 for installation and $36 per month. What is the domain and range for this function?
A.
D = {t € R | 0
B.
D = {x € R | 0
C.
D = {x € R }, R = {f(x) € R }
D.
D = {t € R | 0 0}
Correct Answer A. D = {t € R | 0
Explanation The correct answer is D = {t € R | 0 < t} and R = {f(x) € R | f(x) = 36x + 116}. The domain represents the possible values for the independent variable, which in this case is the number of months. Since the number of months cannot be negative, the domain is all real numbers greater than 0. The range represents the possible values for the dependent variable, which in this case is the total cost. The cost is determined by multiplying the number of months by 36 and adding 116, so the range is all real numbers greater than 116.
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5.
Bowl–o–Mat charges $3.50 per person per game plus $2 per person for show rental. What is the domain of this situation?
A.
Number of players
B.
Total cost per game
C.
Number of games
D.
Cost of shoes
Correct Answer C. Number of games
Explanation The domain of this situation is the number of games. The question is asking about the range of possible values for the number of games that can be played at Bowl-o-Mat. The other options mentioned (number of players, total cost per game, cost of shoes) are not relevant to determining the domain in this scenario.
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6.
Kylie is making a rectangular picture frame. She has 84 cm of ribbon to trim the edges of the frame. She will not use ribbon on the bottom edge of the frame. What is the range for the function of the area of the frame?
A.
R = {0
B.
R = {21
C.
R = {0
D.
R = {42
Correct Answer C. R = {0
Explanation The range for the function of the area of the frame is {0}. This means that the area of the frame can only be 0, indicating that Kylie does not have enough ribbon to make a frame with non-zero area. The fact that she will not use ribbon on the bottom edge of the frame further limits the possible area of the frame.
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7.
What is the domain and range of the quadratic function represented by the following table of values?
A.
D = {x € R | 0
B.
D = {x € R | –8
C.
D = {x € R | –5
D.
D = {x € R | –5
Correct Answer C. D = {x € R | –5
Explanation The domain of the quadratic function represented by the given table of values is all real numbers. This is because there are no restrictions on the values of x in the table. The range of the quadratic function is {y € R | y ≥ -5}. This is because the lowest y-value in the table is -5, and the function can take on any value greater than or equal to -5.
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8.
Which graph shows the range R = {y € R | y => 1}
A.
Y = (x + 1)^2 + 2
B.
Y = (x – 2)^2 + 1
C.
Y = 1
D.
Y = (x – 1)^2 + 1
Correct Answer B. Y = (x – 2)^2 + 1
Explanation The graph y = (x - 2)^2 + 1 represents the range R = {y € R | y > 1} because the vertex of the parabola is at (2, 1), which is the lowest point of the graph. This means that all values of y on the graph are greater than 1. Additionally, as x approaches positive or negative infinity, y also approaches positive infinity, satisfying the condition y > 1. Therefore, this graph accurately represents the given range.
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9.
A golf ball is hit out of a sand trap. The height of the ball is modeled by the function h(t) = –5t^{2} + 6t – 1, where t is time in seconds. What is the maximum height height of the gold ball?
A.
0.6m
B.
0.8m
C.
1.0m
D.
8.0m
Correct Answer B. 0.8m
Explanation The maximum height of the golf ball can be determined by finding the vertex of the parabolic function h(t) = -5t^2 + 6t - 1. The vertex of a parabola represents the maximum or minimum point of the function. In this case, the coefficient of t^2 is negative, indicating that the parabola opens downwards and the vertex represents the maximum height. The formula for finding the x-coordinate of the vertex of a parabola is given by x = -b/2a, where a and b are the coefficients of the quadratic equation. Plugging in the values from the given function, we get x = -6/(2*(-5)) = 0.6. Substituting this value back into the function, we get h(0.6) = -5(0.6)^2 + 6(0.6) - 1 = 0.8. Therefore, the maximum height of the golf ball is 0.8m.
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10.
For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.
A.
D: {1, -3, -4,}
R: {0, 1, 2, -4}
B.
D:{0, 1, 2, -4}
R:{1, -3, -4}
C.
D:{0, 1, 2, 3, 4}
R:{1, -3, -4}
D.
D:{1, 2, 3, 4, 5}
R:{-1, 0, 1, -3, -4}
Correct Answer B. D:{0, 1, 2, -4}
R:{1, -3, -4}
Explanation The domain of a function refers to the set of all possible input values, or x-values, for the function. In this case, the given function has input values of 0, 1, 2, and -4, so the domain is {0, 1, 2, -4}.
The range of a function refers to the set of all possible output values, or y-values, for the function. Looking at the given function, the corresponding output values are 1, -3, and -4, so the range is {1, -3, -4}.
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