Unit1 Test - Functions (General Mathematics 11)

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input has exactly one output. This can be checked using the vertical line test on a graph.

Front

What is the difference between (f + g)(x) and (f - g)(x)?

Back

(f + g)(x) is the sum of the functions f and g evaluated at x, while (f - g)(x) is the difference of the functions f and g evaluated at x.

Front

How do you find (f ⋅ g)(x)?

Back

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

Front

What does it mean to compose functions, such as g(f(x))?

Back

Composing functions means applying one function to the result of another function. g(f(x)) means you first apply f to x, then apply g to the result.

Front

What is the formula for the difference of two functions, (f - g)(x)?

Back

The formula for the difference of two functions is (f - g)(x) = f(x) - g(x).

Front

What is the formula for the product of two functions, (f ⋅ g)(x)?

Back

The formula for the product of two functions is (f ⋅ g)(x) = f(x) * g(x).

Front

What is the significance of the output of g(f(-1)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

The output of g(f(-1)) indicates the value of g when the input is the output of f at -1, demonstrating function composition.

Front

What is the output of the function f(x) = 3x^2 + 7x at x = 3?

Back

To find f(3), substitute 3 into the function: f(3) = 3(3^2) + 7(3) = 27 + 21 = 48.

Front

What is the output of the function g(x) = 2x^2 - x - 1 at x = 2?

Back

To find g(2), substitute 2 into the function: g(2) = 2(2^2) - 2 - 1 = 8 - 2 - 1 = 5.