IM3 midterm

Front

What is the composition of functions g(f(x)) if f(x) = 2x - 8 and g(x) = 4x?

Back

g(f(x)) = 4(2x - 8) = 8x - 32.

Front

What is the transformation of the function f(x) = x^3 to obtain g(x)?

Back

g(x) = (x - 1)^3 represents a horizontal shift to the right by 1 unit.

Front

Back

x = 36.

Front

What does it mean to evaluate a function?

Back

To evaluate a function means to find the output value for a given input.

Front

Back

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

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

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax^2 + bx + c.

Front

What is the formula for the composition of two functions?

Back

The composition of functions f and g is given by (f ∘ g)(x) = f(g(x)).

Front

What is the inverse of the function f(x) = 3x + 2?

Back

The inverse function is f^(-1)(x) = (x - 2)/3.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0.