
Exponential Functions and Graphs
Flashcard
•
Mathematics
•
KG
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is an exponential function?
Back
An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.
2.
FLASHCARD QUESTION
Front
What happens to the value of an exponential function as 'x' increases?
Back
As 'x' increases, the value of the exponential function increases rapidly if 'b' > 1, or decreases rapidly if '0 < b < 1.
3.
FLASHCARD QUESTION
Front
What is the base in an exponential function?
Back
The base is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.
4.
FLASHCARD QUESTION
Front
If you start with $10 and it doubles every year, how much will you have after 3 years?
Back
$80.
5.
FLASHCARD QUESTION
Front
What is the general shape of the graph of an exponential function with a base greater than 1?
Back
The graph rises steeply to the right and approaches the x-axis to the left.
6.
FLASHCARD QUESTION
Front
What is the y-intercept of the exponential function f(x) = 2^x?
Back
The y-intercept is (0, 1) because f(0) = 2^0 = 1.
7.
FLASHCARD QUESTION
Front
What does it mean for a function to be exponential growth?
Back
Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases.
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