Transformations of Linear Functions

Front

What is a transformation of a linear function?

Back

A transformation of a linear function involves changing its position, slope, or both on the coordinate plane, which can include shifts, stretches, and reflections.

Front

What does it mean to shift a graph to the left?

Back

Shifting a graph to the left means that every point on the graph moves horizontally to the left by a certain number of units, which is represented by adding a positive value inside the function's argument.

Front

What does it mean to shift a graph down?

Back

Shifting a graph down means that every point on the graph moves vertically downward by a certain number of units, which is represented by subtracting a value from the function.

Front

How does changing the slope of a linear function affect its graph?

Back

Changing the slope of a linear function affects the steepness of the graph; a larger slope results in a steeper line, while a smaller slope results in a less steep line.

Front

What is the effect of multiplying a linear function by a factor greater than 1?

Back

Multiplying a linear function by a factor greater than 1 results in a vertical stretch of the graph, making it steeper.

Front

What is the effect of multiplying a linear function by a factor between 0 and 1?

Back

Multiplying a linear function by a factor between 0 and 1 results in a vertical shrink of the graph, making it less steep.

Front

What does the y-intercept of a linear function represent?

Back

The y-intercept of a linear function represents the point where the graph intersects the y-axis, indicating the value of the function when x = 0.

Front

How do you represent a vertical shift in a linear function?

Back

A vertical shift in a linear function is represented by adding or subtracting a constant from the function, affecting the y-values.

Front

What is the general form of a linear function?

Back

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

Front

What happens to the graph of f(x) = x when you replace it with f(x) = x + c?

Back

Replacing f(x) = x with f(x) = x + c shifts the graph vertically by c units; if c is positive, it shifts up, and if c is negative, it shifts down.