EOC Flashcard #3 A2B

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f∘g)(x), is defined as f(g(x)). It involves applying one function to the result of another function.

Front

Given g(x)=3x+4 and h(x)=3x-1, find (g∘h)(x).

Back

(g∘h)(x) = g(h(x)) = g(3x-1) = 3(3x-1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

What is the definition of an even function?

Back

A function f(x) is even if for all x in the domain, f(-x) = f(x). This means the graph is symmetric about the y-axis.

Front

What is the definition of an odd function?

Back

A function f(x) is odd if for all x in the domain, f(-x) = -f(x). This means the graph is symmetric about the origin.

Front

Given f(x) = 2x and g(x) = x^2 + 3, find f(g(x)).

Back

f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^{-1}(x) such that f(f^{-1}(x)) = x for all x in the range of f.

Front

Find the inverse of f(x) = x^3 - 5.

Back

f^{-1}(x) = oot{3}{x + 5}.

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.

Front

What is the general form of an exponential regression equation?

Back

The general form of an exponential regression equation is Y = a * b^X, where a is the initial value and b is the growth factor.

Front

How do you determine if a function is even, odd, or neither?

Back

To determine if a function is even, check if f(-x) = f(x). For odd, check if f(-x) = -f(x). If neither condition holds, the function is neither.