Transformations of Functions PRECALCULUS

Front

What is the definition of an even function?

Back

A function is considered even if its graph is symmetric with respect to the y-axis, meaning that f(x) = f(-x) for all x in the domain.

Front

What is the general form of a polynomial function?

Back

A polynomial function is expressed as P(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

How do you determine if a polynomial function is even or odd?

Back

To determine if a polynomial function is even, check if f(x) = f(-x). To determine if it is odd, check if f(-x) = -f(x). If neither condition is met, the function is neither even nor odd.

Front

What is a horizontal shift in the context of function transformations?

Back

A horizontal shift occurs when the graph of a function is moved left or right along the x-axis. For example, f(x - h) shifts the graph h units to the right, while f(x + h) shifts it h units to the left.

Front

What is a vertical shift in the context of function transformations?

Back

A vertical shift occurs when the graph of a function is moved up or down along the y-axis. For example, f(x) + k shifts the graph k units up, while f(x) - k shifts it k units down.

Front

What is the effect of a negative sign in front of a function?

Back

A negative sign in front of a function, such as -f(x), reflects the graph of the function across the x-axis.

Front

What is the transformation that occurs when a function is multiplied by a constant greater than 1?

Back

When a function is multiplied by a constant greater than 1, it results in a vertical stretch of the graph.

Front

What is the transformation that occurs when a function is multiplied by a constant between 0 and 1?

Back

When a function is multiplied by a constant between 0 and 1, it results in a vertical compression of the graph.

Front

How do you represent a horizontal shift of a quadratic function?

Back

A horizontal shift of a quadratic function can be represented as g(x) = f(x - h), where h is the number of units shifted to the right (if h > 0) or to the left (if h < 0).

Front

How do you represent a vertical shift of a quadratic function?

Back

A vertical shift of a quadratic function can be represented as g(x) = f(x) + k, where k is the number of units shifted up (if k > 0) or down (if k < 0).