Algebraic Reasoning Unit 5 Review
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an asymptote in the context of exponential functions?
Back
An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically the line y = 0.
2.
FLASHCARD QUESTION
Front
How do you identify the y-intercept of an exponential function?
Back
The y-intercept of an exponential function f(x) = a(b)^x is found by evaluating f(0), which gives the point (0, a).
3.
FLASHCARD QUESTION
Front
What is the general form of an exponential decay function?
Back
The general form is f(t) = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.
4.
FLASHCARD QUESTION
Front
What does the base of an exponential function indicate?
Back
The base indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.
5.
FLASHCARD QUESTION
Front
How do you determine the x-intercept of an exponential function?
Back
Exponential functions do not have x-intercepts because they never cross the x-axis; they approach it asymptotically.
6.
FLASHCARD QUESTION
Front
What is the significance of the y-intercept in the function f(x) = 3(2)^x?
Back
The y-intercept is the value of the function when x = 0, which is f(0) = 3(2)^0 = 3, indicating the starting value of the function.
7.
FLASHCARD QUESTION
Front
What is the formula for exponential growth?
Back
The formula for exponential growth is f(t) = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.
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