Unit1 Test - Functions (General Mathematics 11)

Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set, called the domain.

Front

What does it mean to find (f - g)(x) for two functions f(x) and g(x)?

Back

Finding (f - g)(x) means subtracting the output of g(x) from the output of f(x) for each x in the domain.

Front

How do you evaluate (f ⋅ g)(x) for two functions f(x) and g(x)?

Back

To evaluate (f ⋅ g)(x), multiply the outputs of f(x) and g(x) for the same input x.

Front

What is the composition of functions, denoted as g(f(x))?

Back

The composition of functions g(f(x)) means to apply function f to x first, and then apply function g to the result of f(x).

Front

How do you find the value of g(f(-1))?

Back

First, evaluate f(-1) to get a value, then substitute that value into g to find g(f(-1)).

Front

What is the significance of evaluating a function at a specific point, such as f(-1)?

Back

Evaluating a function at a specific point gives the output value of the function for that input, which can be used to understand the function's behavior.

Front

What are the restrictions on the domain of a function, such as in f(x)/g(x)?

Back

Restrictions on the domain occur when the function is undefined for certain input values, such as division by zero.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the roots of a quadratic equation in the form ax^2 + bx + c = 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its derivative is positive over an interval and decreasing if its derivative is negative over that interval.