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Course: Algebra 2>Unit 9

Lesson 8: Graphs of logarithmic functions

Transformations of functions: FAQ

What do we mean by "shifting functions horizontally?"

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 $f\left(x\right)={x}^{2}$ three units to the left, we would write $f\left(x+3\right)=\left(x+3{\right)}^{2}$.

What do we mean by "shifting functions vertically?"

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 $f\left(x\right)={x}^{2}$ four units up, we would write $f\left(x\right)={x}^{2}+4$.

How do we reflect a function?

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.

How do we scale a function?

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 $\frac{1}{2}$, we're making it half as tall.

Are there any real-world applications for these transformations?

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.

Want to join the conversation?

• How to you find the vertical asymptote?
• The vertical asymptote of a logarithmic function occurs when the "argument" of the logarithm equals zero.

For example, in the function log(x+4), the argument is (x+4). What does "x" have to be for the argument to equal 0? We can write this as an equation to solve:
x + 4 = 0
Subtract 4 from both sides of the equation.
x = -4.

The vertical asymptote is -4.

In a nutshell, the vertical asymptote is the number that "x" must equal for the argument to equal 0.