Questions and Answers
Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall?
d.h(3) - h(0) / 3
What is the average speed between 2 seconds and 8 seconds?
0.5 meters per second
If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?
30
Which 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 the soup if it varies directly with the number of cans?
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The average rate of change in T(d) for the interval d = 4 and d = 10 is 0. What must be true?
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Which relation is a direct variation that contains the ordered pair (2, 7)?
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The average rate of change of g(x) between x = 4 and x = 7 is 5/6. What must be true?
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What is the average rate of change in Maria's graph of B(t) between t = 3 and t = 7 if it 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 when 10b=5(c+2) is solved for c?
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Which graph represents the same relation as the rule y = 2x?
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Given f(x)=10-2x, find f(7).
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Given b(x)=|x+4|, what is b(-10)?
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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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Given h(f)=-2(t+5)^2+4, find h(-8).
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Which graph represents the same relation as the 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 and Direct Variation
- Height of a falling object is modeled by the function h(t) = 300 - 16t²; average rate for the first 3 seconds uses the expression (h(3) - h(0)) / 3.
- Average speed of a ball thrown is calculated as 0.5 meters per second between 2 and 8 seconds.
Direct Variation Problems
- When y varies directly as x: if y = 180 when x = n, and y = n when x = 5, then n = 30.
- If y is 48 when x is 6, the expression for y when x is 2 is y = (48/6) * 2.
Calculating Average Rate of Change
- Average rate of change in f(x) over an interval [2, 9] is given as (f(9) - f(2)) / (9 - 2).
- For movie ticket sales, if the average rate of change T(d) from day 4 to day 10 is 0, the same number of tickets was sold on both days.
Graphs and Functions
- A direct variation containing the ordered pair (2, 7) is represented by the equation y = (7/2)x.
- Average rate of change of g(x) between x = 4 and x = 7 equals 5/6 implies g(7) - g(4) = (5/6)(7 - 4).
Temperature and Volume Functions
- For Maria's temperature graph B(t), the average rate of change being 8 from t = 3 to t = 7 indicates a 32 degrees increase.
- The formula for the volume of a sphere is V = (3/4)πr³; solving for r leads to the relationship needed to isolate r.
Evaluating Functions and Relations
- f(x) = 10 - 2x evaluated at x = 7 results in -4.
- b(x) = |x + 4| when x = -10 results in b(-10) = 6.
- Given a relation, the alternative representation in a table corresponds to the set {(-6, 4), (-4, 0), (-3, 2), (-1, 2)}.
Other Functions and Notations
- The function h(f) is described by h(f) = -2(t + 5)² + 4; when h(-8) is calculated, it equals -14.
- A one-to-one function is defined within specified relations, ensuring distinct output for each input.
- The range of the graphed function provided is noted as -3.
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Description
These flashcards cover essential concepts related to the rate of change in algebra, specifically tailored for Algebra II students. Learn how to analyze functions and compute average rates based on given scenarios involving falling objects and projectile motion.
