Skills Check 5.1b: Using Exponential Functions

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Mathematics
•
9th - 12th Grade
•
Hard
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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 the base (a positive real number), and 'x' is the exponent.
2.
FLASHCARD QUESTION
Front
What is the horizontal asymptote of an exponential function?
Back
The horizontal asymptote of an exponential function is a horizontal line that the graph approaches as x approaches positive or negative infinity. For functions of the form f(x) = a * b^x + k, the horizontal asymptote is y = k.
3.
FLASHCARD QUESTION
Front
What does it mean for a function to exhibit exponential growth?
Back
Exponential growth occurs when a quantity increases at a rate proportional to its current value, resulting in a rapid increase over time. The graph of an exponential growth function rises steeply.
4.
FLASHCARD QUESTION
Front
What does it mean for a function to exhibit exponential decay?
Back
Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time. The graph of an exponential decay function falls steeply.
5.
FLASHCARD QUESTION
Front
What is the y-intercept of an exponential function?
Back
The y-intercept of an exponential function is the value of the function when x = 0. For f(x) = a * b^x, the y-intercept is f(0) = a.
6.
FLASHCARD QUESTION
Front
What is the range of an exponential growth function?
Back
The range of an exponential growth function is (k, ∞) where k is the horizontal asymptote.
7.
FLASHCARD QUESTION
Front
What is the range of an exponential decay function?
Back
The range of an exponential decay function is (0, k) where k is the horizontal asymptote.
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