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

Front

What does it mean to reflect a function over the y-axis?

Back

Reflecting a function over the y-axis means to create a mirror image of the graph across the y-axis. For a function y = f(x), the reflected function is y = f(-x).

Front

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

Back

The slope of the linear function changes sign when reflected over the y-axis.

Front

What is a vertical translation of a function?

Back

A vertical translation moves the graph of a function up or down without changing its shape. This is done by adding or subtracting a constant from the function.

Front

If a linear function y = mx + b is translated upwards by k units, what is the new equation?

Back

The new equation is y = mx + (b + k).

Front

What is a horizontal translation of a function?

Back

A horizontal translation moves the graph of a function left or right. This is done by adding or subtracting a constant from the x-variable.

Front

If a linear function y = mx + b is translated to the right by h units, what is the new equation?

Back

The new equation is y = m(x - h) + b.

Front

What does it mean to compress a function horizontally?

Back

Compressing a function horizontally means to squeeze the graph towards the y-axis, which increases the slope of the function.

Front

If a linear function y = mx + b is horizontally compressed by a factor of c, what is the new equation?

Back

The new equation is y = m(c*x) + b.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means to create a mirror image of the graph across the x-axis. For a function y = f(x), the reflected function is y = -f(x).