Advanced Algebra Final Exam

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^-1(y) takes y back to x.

Tags

CCSS.HSF-BF.B.4A

Front

If f(x) = 2x + 3, what is f^-1(x)?

Back

To find the inverse, swap x and y: y = 2x + 3. Solve for x: x = 2y + 3 -> y = (x - 3)/2. Thus, f^-1(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

Front

What points does f^-1(x) go through if f(x) goes through (1, 4) and (4, 6)?

Back

f^-1(x) goes through (4, 1) and (6, 4).

Tags

CCSS.HSF-BF.B.4C

Front

What is the relationship between a function and its inverse?

Back

If f and g are inverse functions, then f(g(x)) = x and g(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

If f(2) = -1, what is g(-1)?

Back

g(-1) = 2, since g is the inverse of f.

Tags

CCSS.HSF-BF.B.4C

Front

What is the formula for exponential growth?

Back

The formula is n = n₀ * e^kt, where n₀ is the initial amount, k is the growth rate, and t is time.

Tags

CCSS.HSF-LE.A.1A

Front

If a cell doubles every hour, what function represents the number of cells after h hours if starting with 4 cells?

Back

n = 4(2)^h.

Tags

CCSS.HSF.LE.A.2

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning f(a) = f(b) implies a = b.

Front

How do you find the inverse of a function given in a table?

Back

To find the inverse, swap the input and output values in the table.

Tags

CCSS.HSF-BF.B.4C

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Tags

CCSS.HSF-BF.B.4C