A1-U3.3a Lesson Check: Transforming Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean to transform a linear function?

Back

Transforming a linear function involves changing its position or shape on the graph without altering its linearity. This can include shifting, stretching, or compressing the function.

Front

How does subtracting a value from x affect the graph of a linear function?

Back

Subtracting a value from x shifts the graph of the linear function to the right.

Front

How does adding a value to x affect the graph of a linear function?

Back

Adding a value to x shifts the graph of the linear function to the left.

Front

What is the effect of increasing the coefficient of x in a linear function?

Back

Increasing the coefficient of x makes the slope steeper, resulting in a more vertical line.

Front

What happens to the graph of a linear function when a constant is added to it?

Back

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

Front

What happens to the graph of a linear function when a constant is subtracted from it?

Back

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

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by the coefficient of x in the function's equation.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the constant term b in the equation f(x) = mx + b.

Front

How do you determine the direction of a linear function's slope?

Back

If the slope (m) is positive, the line rises from left to right; if negative, it falls from left to right.