QuestionIndicate whether the following statements are true or false.
A periodic graph repeats itself at regular intervals.
Choose...
The period of a periodic function is equal to twice the length of one cycle.
Choose...
Choose...
The period of the graph above is 6 .
Studdy Solution
STEP 1
What is this asking?
We're checking if some statements about periodic graphs are true or false, and we need to find the period of a specific graph!
Watch out!
Don't mix up the definitions of *cycle* and *period*!
A cycle is one complete pattern, and the period is the *length* of that pattern.
STEP 2
1. Periodic Graphs
2. Period Length
3. Graph's Period
STEP 3
A *periodic graph* repeats itself at regular intervals.
This means the same pattern shows up over and over again.
So, the statement "A periodic graph repeats itself at regular intervals" is **absolutely true**!
STEP 4
The *period* of a periodic function is the **length** of one complete cycle.
The statement says the period is *twice* the length of one cycle.
That's not right!
It's just the length of *one* cycle.
So, this statement is **false**!
STEP 5
Looking at the graph, we can see one complete cycle starts at, let's say, , goes up to its peak, down to its trough, and back to the same height at .
STEP 6
The **length** of this cycle is .
So, the period of the graph is indeed **6**!
The statement "The period of the graph above is 6" is **true**!
STEP 7
1. True
2. False
3. True. The period of the graph is **6**.
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