# Understanding Periodic Functions: Solving for f(7) Given Specific Values of f(x)

• ms. confused
In summary, the given problem involves determining the value of a function f(7) based on the given information about its period and values at specific points. The concept of a periodic function and its definition of having a repeating pattern is key to solving the problem. By understanding the definition of a period and how it applies to the given points, the value of f(7) can be determined.
ms. confused
"The period of function f is 5. If f(1)= 4, f(2)= 5, and f(4)= -2, what is the value of f(7)?"

I'm pretty sure this has something to do with function f(x) as a periodic function when a number p>0 exists, such that for all x in the domain of f, f(x + p) = f(x). I don't understand how this works. Maybe for the first one it sort of makes sense, but the rest of them don't follow the same pattern. I really appreciate any help I could get on this. Thanks.

From what I can tell, it's a simple problem trying to get you to think about what a period is. Just think, what happens in one period of a repetitive function. Also another hint:
sin 0 = ?
sin 2pi = ?
sin 4pi = ?

Along the lines of what Minger said, think about what the definition of "period" is. It is the "time" it takes your function to complete 1 full cycle. So, if the period is 5, that means you can say it has 5 points in it and then it REPEATS. If points 1-5 are the first cycle and then it REPEATS, what can you say about point #7?

## What is a "Weird Trig Graph Question"?

A "Weird Trig Graph Question" is a mathematical problem that involves graphing trigonometric functions in an unusual or unexpected way.

## Why do people find "Weird Trig Graph Questions" difficult?

People find "Weird Trig Graph Questions" difficult because they require a strong understanding of trigonometric functions and their properties, as well as the ability to think critically and creatively.

## What strategies can help solve "Weird Trig Graph Questions"?

Some strategies that can help solve "Weird Trig Graph Questions" include identifying key points on the graph, using symmetry and periodicity properties of trigonometric functions, and breaking the problem down into smaller, more manageable parts.

## Are "Weird Trig Graph Questions" important in real life?

While "Weird Trig Graph Questions" may not have direct applications in everyday life, the skills and concepts learned from solving them can be useful in fields such as engineering, physics, and computer science.

## How can I improve my skills in solving "Weird Trig Graph Questions"?

Practice and familiarity with trigonometric functions and their properties is key to improving skills in solving "Weird Trig Graph Questions". Additionally, seeking out challenging problems and working through them systematically can also help improve problem-solving abilities.

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