Linear and Nonlinear Functions – Practice Problems

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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.


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Exercises in this Practice Problem
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.