Vertical Linear Transformations

Front

What is a vertical linear transformation?

Back

A vertical linear transformation is a change in the position of a graph that moves it up or down along the y-axis without altering its shape.

Front

If f(x) = x, what does g(x) = 2x + 4 represent in terms of vertical transformation?

Back

g(x) = 2x + 4 represents a vertical shift of the graph of f(x) = x upwards by 4 units.

Front

How does the coefficient of x in a linear function affect its graph?

Back

The coefficient of x affects the slope of the graph, but does not affect vertical shifts.

Front

What happens to the graph of f(x) when a constant is added to it?

Back

Adding a constant to f(x) shifts the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

If g(x) = f(x) + k, what does k represent?

Back

k represents the vertical shift of the graph. If k > 0, the graph shifts up; if k < 0, it shifts down.

Front

What is the effect of a negative constant in a vertical transformation?

Back

A negative constant shifts the graph downwards along the y-axis.

Front

If the graph of f(x) is shifted up by 3 units, what is the new function?

Back

The new function is g(x) = f(x) + 3.

Front

What does it mean if a graph is said to be 'shifted down'?

Back

It means that every point on the graph has been moved down by a certain number of units.

Front

How can you determine the direction of a vertical shift from a function?

Back

You can determine the direction of a vertical shift by looking at the constant added or subtracted from the function.

Front

If f(x) = x and g(x) = x - 5, how is g(x) related to f(x)?

Back

g(x) is the graph of f(x) shifted down by 5 units.