Transformations of Linear Functions

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x.

Front

What effect does multiplying a function by a factor greater than 1 have on its graph?

Back

It results in a vertical stretch of the graph.

Front

What does it mean to translate a function down by a certain value?

Back

It means to shift the entire graph of the function downward by that value.

Front

How does the equation y = f(x + c) affect the graph of f(x)?

Back

It translates the graph of f(x) to the left by c units.

Front

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

Back

It represents a reflection of the graph of f(x) across the x-axis.

Front

What is the effect of adding a constant to a function, such as in y = f(x) + k?

Back

It translates the graph of the function vertically by k units.

Front

How does the equation y = 3f(x) - 2 transform the graph of f(x)?

Back

It vertically stretches the graph by a factor of 3 and translates it down by 2 units.

Front

What does a vertical shift of a graph mean?

Back

It means moving the entire graph up or down without changing its shape.

Front

What is the result of the transformation y = f(x) - 5?

Back

The graph of f(x) is shifted down 5 units.

Front

How does the equation y = f(x - 4) affect the graph of f(x)?

Back

It translates the graph of f(x) to the right by 4 units.