QuestionThee graph of a periodic function has a period of 20 , an amplitude of 6 , and whose equation of the axis is 10 . The minimum value of the function is: a) 3 b) 5 c) 4 d) 6
Studdy Solution
STEP 1
What is this asking? Find the lowest point of a wavy function that goes up and down within a certain range. Watch out! Don't mix up the *period* (how long it takes for the wave to repeat) with the *amplitude* (how high the wave goes from the middle).
STEP 2
1. Understand Amplitude
2. Find the Minimum
STEP 3
Alright, so we've got this wavy function, right?
It goes up and down, up and down.
The *amplitude* tells us how far it goes up or down from the middle.
Think of it like swinging – the amplitude is how far you swing from the lowest point to the highest point, divided by two!
STEP 4
In our case, the *amplitude* is **6**.
This means the function goes **6** units *above* the middle line and **6** units *below* the middle line.
STEP 5
The problem tells us the *equation of the axis* is **10**.
This is the middle line of our wavy function.
It's like the resting position of the swing.
STEP 6
Since the *amplitude* is **6**, the lowest point of the function will be **6** units *below* the middle line.
So, we take the middle line value (**10**) and subtract the *amplitude* (**6**):
STEP 7
So, the minimum value of the function is **4**!
STEP 8
The minimum value of the function is **4**, which is option (c).
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