Transformations of Linear Functions Flashcard

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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally or vertically without changing its shape.

Front

What is the effect of translating a linear function 4 units to the right?

Back

To translate a linear function 4 units to the right, you replace x with (x - 4) in the function's equation.

Front

What happens to the equation of a linear function when it is reflected over the x-axis?

Back

When a linear function is reflected over the x-axis, the sign of the slope (m) changes, resulting in the equation y = -mx + b.

Front

How do you vertically stretch a linear function by a factor of 2?

Back

To vertically stretch a linear function by a factor of 2, you multiply the entire function by 2, resulting in y = 2(mx + b).

Front

What is the new equation when y = 2x - 5 is translated 4 units to the right and reflected over the x-axis?

Back

The new equation is y = -2(x - 4) + 5.

Front

What does it mean to compress a function horizontally?

Back

Compressing a function horizontally means to squeeze its graph towards the y-axis, which involves multiplying the x variable by a factor less than 1.

Front

What is the new equation when y = 5x + 1 is horizontally compressed by a factor of 3?

Back

The new equation is y = 5(x/3) + 1.

Front

What is the effect of reflecting a linear function over the y-axis?

Back

Reflecting a linear function over the y-axis changes the sign of the x-coefficient in the equation.

Front

What is the new equation when y = 4x - 1 is reflected over the y-axis?

Back

The new equation is y = -4x - 1.