M3 Mid Exam Function Transformations Compositions Inverses

Front

What is a transformation in the context of functions?

Back

A transformation refers to the alteration of a function's graph through shifts, stretches, compressions, or reflections.

Front

Describe the effect of the transformation p(x) = f(x + 3).

Back

This transformation shifts the graph of f(x) left by 3 units.

Front

What does a reflection over the x-axis do to a function?

Back

It inverts the y-values of the function, changing f(x) to -f(x).

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch multiplies the function's output by a factor greater than 1, making the graph taller.

Front

How do you represent a reflection over the y-axis in a function?

Back

To reflect a function over the y-axis, replace x with -x in the function's equation.

Front

What is the composition of functions?

Back

The composition of functions involves applying one function to the result of another, denoted as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = 1/x and g(x) = 3x + 2, what is f(g(x))?

Back

f(g(x)) = \frac{1}{3x + 2}.

Front

What does the notation g(x) = sqrt(-x - 8) indicate about the function's reflection?

Back

This function is reflected over the y-axis due to the negative sign in front of x.

Front

What is the general form of a quadratic function?

Back

A quadratic function is generally expressed as f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you determine the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and substituting back to find the y-coordinate.