Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the form of the function, such as shifting, stretching, compressing, or reflecting it.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x².

Front

How does the coefficient of a quadratic function affect its graph?

Back

If the coefficient is greater than 1, the graph is narrower than the parent function. If it is between 0 and 1, the graph is wider.

Front

What happens to the vertex of a function when it is shifted horizontally?

Back

The x-coordinate of the vertex changes according to the direction and magnitude of the shift.

Front

What is the effect of a vertical shift on the graph of a function?

Back

A vertical shift moves the graph up or down without changing its shape.

Front

How do you reflect a function over the x-axis?

Back

To reflect a function over the x-axis, multiply the entire function by -1.

Front

What does it mean to stretch a function vertically?

Back

To stretch a function vertically means to multiply the function by a factor greater than 1, making it taller.

Front

What does it mean to compress a function vertically?

Back

To compress a function vertically means to multiply the function by a factor between 0 and 1, making it shorter.

Front

If f(x) = x², what is g(x) = f(x) + 3?

Back

g(x) is the graph of f(x) shifted vertically up by 3 units.

Front

What is the vertex of the function g(x) = f(x + 2) if f(x) has a vertex at (-4, 5)?

Back

The vertex of g(x) is (-6, 5).