Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does f(-x) represent in function transformations?

Back

f(-x) represents a reflection of the graph of f(x) over the y-axis.

Front

What does f(x) + k do to the graph of f(x)?

Back

f(x) + k shifts the graph of f(x) vertically by k units. If k is positive, it shifts up; if k is negative, it shifts down.

Front

What does f(x - h) do to the graph of f(x)?

Back

f(x - h) shifts the graph of f(x) horizontally by h units. If h is positive, it shifts right; if h is negative, it shifts left.

Front

What is the effect of multiplying a function by a negative number, such as -f(x)?

Back

Multiplying a function by a negative number reflects the graph over the x-axis.

Front

What does a vertical stretch of a function mean?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph steeper.

Front

What does a vertical compression of a function mean?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph less steep.

Front

What is the transformation represented by g(x) = f(x) + 3?

Back

The transformation g(x) = f(x) + 3 represents a vertical shift of the graph of f(x) upward by 3 units.

Front

What is the transformation represented by g(x) = f(x - 2)?

Back

The transformation g(x) = f(x - 2) represents a horizontal shift of the graph of f(x) to the right by 2 units.

Front

What does the transformation h(x) = 2f(x) do to the graph of f(x)?

Back

The transformation h(x) = 2f(x) represents a vertical stretch of the graph of f(x) by a factor of 2.