Function Transformations

Front

What is the parent function of linear transformations?

Back

Linear

Front

What transformation does the function m(x) = f(x + 1) represent?

Back

Left 1 unit

Front

Describe the transformation of the function f(x) = (x + 7)² compared to its parent function.

Back

Horizontal shift left 7 units

Front

What transformations occur in the function f(x) = (x - 3)² + 5 from the original function?

Back

Right 3 units and up 5 units

Front

What transformation does the function p(x) = f(x + 3) represent?

Back

Left 3 units

Front

What is a vertical shift in function transformations?

Back

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

Front

How does a horizontal shift affect the graph of a function?

Back

A horizontal shift moves the graph left or right along the x-axis.

Front

What is the effect of a negative sign in front of a function, such as f(x) = -g(x)?

Back

It reflects the graph of the function across the x-axis.

Front

What does the transformation f(x) = g(x) + k represent?

Back

A vertical shift of k units, where k is positive (up) or negative (down).

Front

What is the effect of multiplying a function by a factor greater than 1, such as f(x) = 2g(x)?

Back

It vertically stretches the graph of the function.