IM3 midterm

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f∘g)(x), is the application of one function to the results of another. It is defined as (f∘g)(x) = f(g(x)).

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables in the equation and solve for y. The inverse function undoes the action of the original function.

Front

What is the quadratic function form?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's equation and simplify.

Front

What does it mean for a function to be defined?

Back

A function is defined for a specific input if there is a corresponding output. If an input does not yield an output, the function is undefined at that point.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What transformations occur when a function is shifted right and up?

Back

Shifting a function right by h units and up by k units transforms f(x) to f(x-h) + k.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b^2 - 4ac in the quadratic equation ax^2 + bx + c = 0, determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, express it in the form (x-p)(x-q)=0, then set each factor to zero: x-p=0 and x-q=0.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are reflections of each other across the line y=x. If f(a) = b, then f^(-1)(b) = a.