Math Snap

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):
$$10 - 6 = 4$$

STEP 7

So, the minimum value of the function is 4!

The minimum value of the function is 4, which is option (c).