A function is essentially a slope-intercept equation that has been rewritten to replace y with f(x).
Here’s an example of how this is done:
The purpose of a function is to show how an input (the x-value) impacts an output (the y-value).
Functions are governed by specific rules:
Sometimes, you won’t have a graph or an equation for your function. In cases like these, you would be given a function and a table like this example:
To construct a function from a table, you would first find the slope (see this resource for more information). Then, you would identify the y-intercept (see this resource for more information). Then, you would create the function using the slope-intercept form (see this resource for more information).
Most function problems that you might encounter will likely involve function modeling. You can model a function from the information that’s found in a story problem. This is called translating statements into symbols, as seen here:
Here is a breakdown of how to model and solve a function:
Slope-interception form is the primary method of displaying functions (see this resource for more information). However, there are two other forms that you might see: point-slope form and standard form.
The purpose of point-slope form is to make it easier to plug a coordinate pair into the equation. See this resource on coordinate pairs for more information.
Here’s the template for the point-slope form:
Slope-interception form is the primary method of displaying functions (see this resource for more information). However, there are two other forms that you might see: point-slope form and standard form.
The purpose of standard form is to set up systems of equations (see this resource for more information).
Here’s the template for the standard form:
It’s easy to determine whether lines are parallel or perpendicular when you see the lines on a graph. However, you will often be given functions without graphs and be asked to find out whether the lines are parallel or perpendicular.
Lines that are parallel have the same slope. Here’s an example:
Lines that are perpendicular have slopes that are negative reciprocals of each other (see this resource for more information about reciprocals).
Here’s an example:
A system of equations is a pair of two equations that each have two variables. The variables must be the same between the equations.
Systems of equations can be solved either graphically or by hand. When solving graphically, you would plot the two functions on the graph and find the intersection point like this:
Most problems will require you to solve systems of equations by hand. Here's an example of how to do this:
