Question

Math

Posted 3 months ago

```
Below is the graph of a trigonometric function. It has a minimum point at $(-5.4,1.25)$ and a maximum point at $(7.4,6.75)$.
What is the amplitude of the function?
$\square$ units
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Identify the maximum and minimum y-values of the trigonometric function from the graph

step 2

The maximum y-value is given as $6.75$ and the minimum y-value is given as $1.25$

step 3

Calculate the amplitude of the function, which is the distance between the maximum and minimum y-values divided by 2

step 4

The amplitude is $\frac{6.75 - 1.25}{2}$

step 5

Simplify the calculation to find the amplitude: $\frac{5.5}{2} = 2.75$

[1] Answer

The amplitude of the function is $2.75$ units.

Key Concept

Amplitude of a Trigonometric Function

Explanation

The amplitude of a trigonometric function is the distance from the midline of the function to its maximum or minimum value, which is half the distance between the maximum and minimum y-values of the function.

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