Linear Transformation Flashcard

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which can be transformed to create other functions.

Front

What does it mean to shift a function down?

Back

Shifting a function down means to decrease the output values of the function by a certain amount, moving the graph downward on the coordinate plane.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

How does a steeper line compare to a less steep line?

Back

A steeper line has a greater absolute value of slope compared to a less steep line, indicating it rises or falls more sharply.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function shifts the graph vertically. If the constant is positive, it shifts up; if negative, it shifts down.

Front

What does the equation f(x) = mx + b represent?

Back

This equation represents a linear function, where m is the slope and b is the y-intercept.

Front

What happens to the graph of a function when the slope is increased?

Back

Increasing the slope makes the graph steeper, meaning it rises or falls more quickly.

Front

What is the transformation of the function f(x) = 2x + 3 compared to its parent function f(x) = x?

Back

The function f(x) = 2x + 3 is steeper than the parent function and is shifted up 3 units.

Front

How do you identify a line that is less steep than another?

Back

To identify a line that is less steep, compare the slopes; the line with the smaller absolute value of slope is less steep.

Front

What does it mean for a function to be shifted 7 units up?

Back

It means that every point on the graph of the function is moved vertically upward by 7 units.