Transformation of Linear Functions

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which represents a straight line with a slope of 1 and a y-intercept of 0.

Front

How does a positive slope affect the graph of a linear function?

Back

A positive slope causes the graph to rise from left to right, indicating a direct relationship between x and y.

Front

What does it mean for a function to be 'steeper'?

Back

A function is 'steeper' when its slope is greater than that of another function, meaning it rises or falls more sharply.

Front

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

Back

Adding a positive constant to a linear function shifts the graph upward by that constant value.

Front

What is the effect of subtracting a constant from a linear function?

Back

Subtracting a constant from a linear function shifts the graph downward by that constant value.

Front

What does it mean for two linear functions to have equal slopes?

Back

Two linear functions with equal slopes are parallel to each other and will never intersect.

Front

If a linear function is shifted 3 units up, what is the new function if the original is f(x) = 2x + 1?

Back

The new function is f(x) = 2x + 4.

Front

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

Back

A negative slope causes the graph to fall from left to right, indicating an inverse relationship between x and y.

Front

How can you determine if a linear function has been shifted horizontally?

Back

A horizontal shift occurs when a constant is added or subtracted from the x variable in the function.

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.