

if.6 alg 1
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the average rate of change of a function?
Back
The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value. It is calculated as \( \frac{f(b) - f(a)}{b - a} \) for the interval [a, b].
2.
FLASHCARD QUESTION
Front
How do you calculate the average rate of change for the function \( f(x) = 6(2)^x \) from x = -1 to x = 2?
Back
1. Calculate \( f(-1) = 6(2)^{-1} = 3 \) and \( f(2) = 6(2)^{2} = 24 \). 2. Average rate of change = \( \frac{24 - 3}{2 - (-1)} = \frac{21}{3} = 7 \).
3.
FLASHCARD QUESTION
Front
What is the formula for the average rate of change of a linear function?
Back
For a linear function \( f(x) = mx + b \), the average rate of change is constant and equal to the slope \( m \).
4.
FLASHCARD QUESTION
Front
How do you find the average rate of change of \( f(x) = 5x - 7 \) from x = -3 to x = 7?
Back
1. Calculate \( f(-3) = 5(-3) - 7 = -22 \) and \( f(7) = 5(7) - 7 = 28 \). 2. Average rate of change = \( \frac{28 - (-22)}{7 - (-3)} = \frac{50}{10} = 5 \).
5.
FLASHCARD QUESTION
Front
What is the average rate of change in a real-world context?
Back
In real-world scenarios, the average rate of change can represent speed, growth rate, or any change over time, such as the rate of descent of a diver.
6.
FLASHCARD QUESTION
Front
How do you calculate the average rate of change of Maya's dive from 1 to 2.5 seconds?
Back
1. Determine the height at 1 second and 2.5 seconds. 2. Average rate of change = \( \frac{height_{2.5} - height_{1}}{2.5 - 1} \).
7.
FLASHCARD QUESTION
Front
What is the average rate of change of fruit flies between Day 3 and Day 5 if there were 1900 flies on Day 3 and 7600 on Day 5?
Back
Average rate of change = \( \frac{7600 - 1900}{5 - 3} = \frac{5700}{2} = 2850 \) fruit flies per day.
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