Linear and Nonlinear Functions – Practice Problems
Having fun while studying, practice your skills by solving these exercises!
- Video
- Practice Problems
A linear function is a function with standard form y = mx + b, where m is the slope and b is the y-intercept, and whose graph looks like a straight line.
There are other functions whose graph is not a straight line. These functions are known as nonlinear functions and they come in many different forms.
One such nonlinear function is a quadratic function, which is written in the standard form,
y = ax2 + bx + c.
The graph of a quadratic function is a parabola. The direction in which the parabola opens depends on the coefficient a:
If a is positive, the parabola opens upward.
If a is negative, the parabola thus opens downward.
Another nonlinear function is the cubic function, which is written in the standard form,
y = ax3 + bx2 + cx + d.
The graph of a cubic function look like a sideways S, where the direction S is rotated depends on a:
If a is positive, S is rotated counter-clockwise.
If a is negative, S is rotated clockwise.
Once you know the standard form of a function, it becomes much easier to graph and understand!
Analyze functions using different representations.
CCSS.MATH.CONTENT.HSF.IF.C.7
Identify the parameters of the given linear function. |
Define a quadratic function. |
Decide which functions are linear functions. |
Determine the right function for the graph. |
Find the graphs of different types of functions. |
Find the graphs of the given functions. |