STATION 3: Transformations of Linear Functions

Front

What is a horizontal translation in the context of graph transformations?

Back

A horizontal translation involves shifting the graph of a function left or right along the x-axis without changing its shape.

Front

How does a vertical translation affect the graph of a function?

Back

A vertical translation shifts the graph up or down along the y-axis, changing the function's output values.

Front

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

Back

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, effectively flipping it upside down.

Front

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

Back

Multiplying a function by a negative constant reflects the graph over the x-axis and can also change its steepness.

Front

What does the term 'parent function' refer to?

Back

A parent function is the simplest form of a function in a family of functions, from which other functions can be derived through transformations.

Front

How does adding a constant 'c' to a function f(x) affect its graph?

Back

Adding a constant 'c' to f(x) results in a vertical shift of the graph; if c is positive, the graph shifts up, and if c is negative, it shifts down.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables; a positive slope means the line rises, while a negative slope means it falls.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

How can you identify a vertical translation from a function's equation?

Back

A vertical translation can be identified by the presence of a constant added or subtracted from the function, such as in y = f(x) + c.