Linear Transformations and Parent Function

Front

What is the linear parent function?

Back

The linear parent function is f(x) = x, which represents a straight line with a slope of 1 and passes through the origin.

Front

What does it mean to shift a function left or right?

Back

Shifting a function left or right involves adding or subtracting a value from the input (x) in the function's equation.

Front

If g(x) = f(x + 6), how is the graph of f(x) transformed?

Back

The graph of f(x) is shifted left by 6 units.

Front

What is the effect of adding a constant to the function f(x)?

Back

Adding a constant to f(x) shifts the graph vertically. For example, f(x) + k shifts the graph up by k units if k is positive and down if k is negative.

Front

What is the transformation of f(x) = x when it becomes f(x) = x - 2?

Back

The graph of f(x) = x is shifted down 2 units.

Front

How does the function y = f(x - 4) transform the parent function?

Back

The function y = f(x - 4) shifts the graph of the parent function to the right by 4 units.

Front

What does the transformation f(x) = (x + 5) + 7 represent?

Back

This transformation shifts the graph of the parent function up 7 units and left 5 units.

Front

What is the result of shifting the parent function f(x) = x up by 3 units?

Back

The resulting function is f(x) = x + 3.

Front

If f(x) = x + 4, what transformation has occurred from the parent function?

Back

The graph has been shifted up 4 units.

Front

What does the transformation y = f(x) - 5 do to the graph of f(x)?

Back

It shifts the graph of f(x) down 5 units.