Questions: Day 3 Unit 3 Determining Equations from Graphs 1) (Exemplar) Consider the following graph. a. Determine the following information for the graphed function. (i) Midline (ii) Period (iii) Angular speed (iv) Amplitude

Day 3 Unit 3
Determining Equations from Graphs
1) (Exemplar) Consider the following graph.
a. Determine the following information for the graphed function.
(i) Midline
(ii) Period
(iii) Angular speed
(iv) Amplitude

Transcript text: Day 3 Unit 3 Determining Equations from Graphs 1) (Exemplar) Consider the following graph. a. Determine the following information for the graphed function. (i) Midline (ii) Period (iii) Angular speed (iv) Amplitude

Solution

Solution Steps

Step 1: Find the midline

The midline is the horizontal line that passes exactly in the middle between the graph's highest and lowest points. The highest point the graph reaches is -1, and the lowest point is -7. The middle value is (-1 + (-7))/2 = -4. Therefore, the midline is _y = -4_.

Step 2: Find the period

The period is the horizontal distance it takes for the graph to complete one full cycle. Starting at _x = 0_, the graph completes a full cycle at _x = π_. Therefore, the period is _π_.

Step 3: Find the angular speed

Angular speed ( _ω_ ) is calculated as _ω= 2π / Period_. In our case, the period is _π_. Therefore, the angular speed is _ω = 2π / π = 2_.