Questions and Answers
What expression can be used to determine the average rate at which an object falls during the first 3 seconds of its fall?
d.h(3) - h(0) / 3
What is the average speed of the ball between 2 seconds and 8 seconds?
0.5 meters per second
If y varies directly as x with y being 180 when x is n and y is n when x is 5, what is the value of n?
30
What expression can be used to determine the average rate of change in f(x) over the interval [2, 9]?
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If y varies directly as x and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
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Which graph represents the cost of soup that varies directly with the number of cans?
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What must be true if the average rate of change in T(d) from d = 4 to d = 10 is 0?
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Which relation is a direct variation that contains the ordered pair (2, 7)?
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What is the equation for the average rate of change of g(x) between x = 4 and x = 7?
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What can be concluded if the average rate of change in B(t) from t = 3 to t = 7 is 8?
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What is the formula for the volume of a sphere solved for r?
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What is an equivalent equation to find c if 10b=5(c+2) is solved for c?
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Which graph represents the same relation as the rule y = 2x, for all real numbers x?
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What is the result when finding f(7) for f(x)=10-2x?
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What is b(-10) if b(x)=|x+4|?
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Which table represents the same relation as the set {(-6,4),(-4,0),(-3,2),(-1,2)}?
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What is the result of finding h(-8) if h(f)=-2(t+5)^2+4?
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Which graph represents the same relation as the provided set?
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Which relation below represents a one-to-one function?
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Which graph represents the same relation as the table below?
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What is the range of the function graphed below?
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Study Notes
Rate of Change in Functions
- Height of a falling object modeled by h(t) = 300 - 16t²; average rate of fall in the first 3 seconds calculated using (h(3) - h(0)) / 3.
- Average speed of a ball between 2 seconds and 8 seconds is 0.5 meters per second.
- If y varies directly with x, y is 180 when x is n, and y is n when x is 5; value of n is 30.
Average Rate of Change
- Average rate of change in f(x) over [2, 9] determined by (f(9) - f(2)) / (9 - 2).
- For direct variation, when y is 48 at x = 6, the equation used to find y at x = 2 is y = (48/6)(2).
- Cost of soup varies directly with cans; determined values signify relationships to corresponding graphs.
Ticket Sales and Direct Variation
- For T(d), the average rate of change being 0 implies the same number of tickets sold on the fourth and tenth days.
- Relation that includes the ordered pair (2, 7) in direct variation takes the form y = (7/2)x.
- Average rate of change of g(x) is given by (g(7) - g(4)) / (7 - 4) = 5/6.
Temperature Change and Volume of Sphere
- Maria's temperature function B(t) shows an average rate of change of 8 between t = 3 and t = 7, indicating a temperature increase of 32 degrees.
- Volume of a sphere expressed as V = (3/4)πr³ must be solved for r.
Graphs and Relations
- A graph representing y = 2x must hold true for all real numbers x.
- Evaluations of functions like f(x) = 10 - 2x can yield specific results such as f(7) = -4.
- For b(x) = |x + 4|, calculating b(-10) gives a value of 6.
Functions and Sets
- To represent the same relation as the ordered pair set {(-6,4),(-4,0),(-3,2),(-1,2)}, the correct table matches these coordinates.
- Using h(f) = -2(t + 5)² + 4, finding h(-8) results in -14.
- Identifying a one-to-one function from a list emphasizes unique outputs for every input.
Summary of Range and Relationships
- The range of graphed functions is crucial; example values include -3 for specific functions.
- Various relations like the sets of points and their respective graphs showcase direct correlations and changes in function outputs.
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Description
This quiz focuses on concepts of average rate of change in functions, including the height of falling objects and direct variation. Understand how to calculate average rates and apply direct variation equations to solve problems. Test your knowledge with various scenarios involving rates of change and direct relationships.
