AP Precalculus: Unit 2 Review

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions where the output of one function becomes the input of another. It is denoted 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 f(x), swap the x and y in the equation and solve for y. The inverse is denoted as f^{-1}(x).

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if, as x increases, f(x) also increases. It is decreasing if, as x increases, f(x) decreases.

Front

What is a quadratic function?

Back

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

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set f(x) = 0 and solve the equation ax^2 + bx + c = 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula x = -b/(2a).

Front

What is a transformation of a function?

Back

A transformation of a function involves changing its position, size, or shape. Common transformations include translations, reflections, stretches, and compressions.

Front

What is the effect of multiplying a function by a constant?

Back

Multiplying a function by a constant greater than 1 stretches the graph vertically, while multiplying by a constant between 0 and 1 compresses it vertically.

Front

What is the significance of the horizontal line test?

Back

The horizontal line test determines if a function has an inverse. If any horizontal line intersects the graph more than once, the function does not have an inverse.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse 'undo' each other. If f(x) is a function, then f(f^{-1}(x)) = x and f^{-1}(f(x)) = x.