AP PreCalculus Flashcards: Change in Linear and Exponential Functions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
Linear Function Change
A function is linear if its output values change at a constant rate over equal-length input-value intervals.
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Linear Function Change
A function is linear if its output values change at a constant rate over equal-length input-value intervals.
What is the core similarity between linear functions and arithmetic sequences?
Both can be expressed as an initial value plus the repeated addition of a constant rate of change.
If the output values of a function change at a constant rate over equal-length input intervals, what type of function is it?
If the output values of a function change at a constant rate over equal-length input-value intervals, the function is linear.
What is the fundamental operational difference between linear and exponential functions?
Linear functions are based on repeated addition of a constant rate of change, while exponential functions are based on repeated multiplication by a constant proportion.
A function's values are 10, 20, 40, 80 over four equal intervals. Is this function likely linear or exponential, and why?
The function is exponential because its output values change proportionally (multiplying by 2) over equal intervals.
Describe the difference in how linear and exponential functions grow based on their foundational operation.
Linear functions grow through constant addition, resulting in a steady rate of change, while exponential functions grow through constant multiplication, resulting in a proportional rate of change.
Exponential Function Change
A function is exponential if its output values change proportionally over equal-length input-value intervals.
If the output values of a function change proportionally over equal-length input intervals, what type of function is it?
If the output values of a function change proportionally over equal-length input-value intervals, the function is exponential.
How can functions of real numbers be constructed to be comparable to discrete sequences?
They can be constructed to be comparable to arithmetic and geometric sequences, with linear functions mirroring arithmetic sequences and exponential functions mirroring geometric ones.
What is the core similarity between exponential functions and geometric sequences?
Both can be expressed as an initial value times the repeated multiplication by a constant proportion.
A function's values are 10, 15, 20, 25 over four equal intervals. Is this function likely linear or exponential, and why?
The function is linear because its output values change at a constant rate (adding 5) over equal intervals.
What key property regarding their determination is shared by linear functions, exponential functions, arithmetic sequences, and geometric sequences?
All four have the property that they can be determined by two distinct sequence or function values.
What is the structure of an exponential function and how does it relate to a geometric sequence?
An exponential function, f(x) = ab^{x}, is similar to a geometric sequence, g_{n} = g_{0}r^{n}, as both are expressed as an initial value times repeated multiplication by a constant proportion.
What is the structure of a linear function and how does it relate to an arithmetic sequence?
A linear function, f(x) = b+mx, is similar to an arithmetic sequence, a_{n} = a_{0}+dn, as both are expressed as an initial value plus the repeated addition of a constant.