
Week 16 KA: Identifying and Evaluating Exponential Function

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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 a positive real number, and 'x' is the exponent. The function grows or decays at a constant percentage rate.
2.
FLASHCARD QUESTION
Front
How can you identify an exponential function from a table of values?
Back
You can identify an exponential function by checking if the ratio of consecutive y-values is constant as x increases by equal intervals. If the y-values are multiplied by a constant factor, it is exponential.
3.
FLASHCARD QUESTION
Front
What is a linear function?
Back
A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.
4.
FLASHCARD QUESTION
Front
What does it mean for a function to have a constant rate of change?
Back
A function has a constant rate of change if the difference in y-values divided by the difference in x-values is the same for any two points on the function. This indicates a linear relationship.
5.
FLASHCARD QUESTION
Front
What is a constant factor in the context of exponential functions?
Back
A constant factor in exponential functions refers to the fixed number by which the y-value is multiplied as x increases by 1. For example, if y is multiplied by 3 as x increases by 1, then 3 is the constant factor.
6.
FLASHCARD QUESTION
Front
What is the difference between exponential growth and exponential decay?
Back
Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1, leading to increasing values. Exponential decay occurs when 'b' is between 0 and 1, leading to decreasing values.
7.
FLASHCARD QUESTION
Front
Can a function be both linear and exponential?
Back
No, a function cannot be both linear and exponential. Linear functions have a constant rate of change, while exponential functions have a constant multiplicative factor.
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