Transformations Exit Ticket

Front

What is a translation in the context of function transformations?

Back

A translation is a shift of a graph in a specific direction without changing its shape or orientation.

Front

How does a translation of 3 units to the left affect the function f(x)?

Back

The function f(x) becomes f(x + 3), shifting the graph 3 units left.

Front

What does it mean for a function to be reflected over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the parent function of quadratic functions?

Back

The parent function of quadratic functions is y = x².

Front

How do you identify a vertical shift in a function?

Back

A vertical shift is identified by a constant added or subtracted from the function, e.g., f(x) + k shifts the graph up by k units, while f(x) - k shifts it down.

Front

What transformation occurs in the function y = (x - 2)² + 4?

Back

The graph shifts right 2 units and up 4 units from the parent function.

Front

What is the effect of multiplying a function by a negative number?

Back

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

Front

How does the function y = 2x² + 3 differ from y = 2x²?

Back

The function y = 2x² + 3 is shifted up 3 units from the graph of y = 2x².

Front

What does the notation f(x) = (x + 1)² - 7 indicate about the graph?

Back

This indicates a shift left 1 unit and down 7 units from the parent function.

Front

What is the transformation represented by the function y = -(x + 3)² + 1?

Back

This function is reflected over the x-axis, shifted left 3 units, and shifted up 1 unit.