Function notation is crucial for understanding equations, graphs, parabolas, and polynomials on the SAT. Functions are typically denoted as
Generally, you can treat
When given a function
To find the value of
Simply plug the number in the parentheses into the variable. Easy peasy!
A composite function is essentially a function within a function. There are numerous ways the SAT might test this concept, but understanding it's simplicity can earn you points. Let's look at an example:
If
The process is the same as with numbers: substitute the expression inside the parentheses for the variable.
Now substitute
Let's explore another example.
If
First, break the problem into two parts. Notice, they are not asking for
First, find
Now find
So
On the SAT, you might be given a graph along with its function. Typically, you will be asked about transformations and properties like the x-intercept and y-intercept.
All you need to do is memorize two rules. I’ll use
• If given
• If given
In simpler terms: Outside the parentheses is up and down; inside the parentheses is left and right.
Let's look at some graphs to see this concept in action.
This graph shows
This graph shows
Feel free to use Desmos or any graphing tool to experiment with transforming functions. Practice is the best way to understand and memorize these concepts.
For more on composite functions
Extended video lesson on functions
For more on graph transformations