Final Review

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another function. If F and G are two functions, the composition is denoted as (F ∘ G)(x) = F(G(x)).

Front

Calculate G(F(4)) if F(x) = x - 6 and G(x) = x^2.

Back

G(F(4)) = G(4 - 6) = G(-2) = (-2)^2 = 4.

Front

What is the value of F(G(-1)) if F(x) = 5x - 4 and G(x) = 3x?

Back

F(G(-1)) = F(3(-1)) = F(-3) = 5(-3) - 4 = -15 - 4 = -19.

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

What is the result of (5 + 4i) + (7 - 10i)?

Back

(5 + 4i) + (7 - 10i) = (5 + 7) + (4 - 10)i = 12 - 6i.

Front

What is G(F(2)) if F(x) = 5x - 4 and G(x) = 3x?

Back

G(F(2)) = G(5(2) - 4) = G(10 - 4) = G(6) = 3(6) = 18.

Front

Define a function. What are its key characteristics?

Back

A function is a relation that assigns exactly one output for each input. Key characteristics include domain (set of inputs), range (set of outputs), and the rule that defines the relationship.

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. A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is the point (h, k) where h = -b/(2a) and k = f(h). It represents the maximum or minimum point of the parabola.

Front

Explain the concept of a zero of a function.

Back

A zero of a function is a value of x for which f(x) = 0. It represents the x-intercepts of the graph of the function.