Functions: Evaluation and Operations Flashcard

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (g ∘ f)(x) = g(f(x)).

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's equation. For example, for f(x) = x^2 + 1, to find f(2), substitute 2 for x: f(2) = 2^2 + 1 = 5.

Front

What is the value of f(0) if f(x) = x^2 - 1?

Back

f(0) = 0^2 - 1 = -1.

Front

Given f(x) = x^2 - 1, what is g(f(0)) if g(x) = x + 3?

Back

g(f(0)) = g(-1) = -1 + 3 = 2.

Front

What is the formula for the sum of two functions?

Back

The sum of two functions f and g is defined as (f + g)(x) = f(x) + g(x).

Front

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

Back

(f + g)(-1) = f(-1) + g(-1) = (2(-1) + 3) + ((-1)^2) = 1 + 1 = 2.

Front

What is the value of g(f(2)) if f(x) = x^2 + 1 and g(x) = x - 3?

Back

g(f(2)) = g(5) = 5 - 3 = 2.

Front

How do you find f(g(3)) if f(x) = x^2 + 2x + 1 and g(x) = x - 1?

Back

First, find g(3): g(3) = 3 - 1 = 2. Then, find f(2): f(2) = 2^2 + 2(2) + 1 = 9.

Front

What is the value of f(g(3)) if f(x) = x + 2 and g(x) = 2x - 1?

Back

g(3) = 2(3) - 1 = 5. Then, f(5) = 5 + 2 = 7.

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.