precalc 1.4 BB

Front

What is function composition?

Back

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

Front

Given f(x) = -3x + 7 and g(x) = 2x^2 - 8, find g(f(x)).

Back

g(f(x)) = 18x^2 - 84x + 90.

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

Given j(x) = ∛(x-1) and h(x) = x^3 + 1, find j(h(x)).

Back

j(h(x)) = x.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, where m and b are constants, and its graph is a straight line. A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and its graph is a parabola.

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find f(g(5)).

Back

f(g(5)) = 19.

Front

What is the definition of a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

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

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.