Transformations of functions: FAQ

When we shift a function horizontally, we are moving the entire graph of the function left or right. This is done by adding or subtracting a constant from the function's input. For example, to shift the function $f(x)=x^2$‍ three units to the left, we would write $f(x+3)=(x+3{)}^2$‍.

Vertical shifting is similar to horizontal shifting, except we are moving the entire graph of the function up or down. This is done by adding or subtracting a constant from the function's output. For example, to shift the function $f(x)=x^2$‍ four units up, we would write $f(x)=x^2+4$‍.

When we reflect a function, we're flipping it over a specific line. For example, if we reflect a function over the $y$‍-axis, we're flipping it from left to right. If we reflect a function over the $x$‍-axis, we're flipping it from top to bottom.

When we scale a function, we're changing its size on the graph. For example, if we multiply a function by $2$‍, we're making it twice as tall. If we multiply a function by ${\displaystyle \frac{1}{2}}$‍, we're making it half as tall.

Yes! We use transformations in a variety of fields, like engineering, physics, and economics. For example, in physics, we often use transformations to change the units of a function in order to make it easier to work with. In economics, we might use transformations to help us compare different data sets.