f(x)=Asin(Bx-C)+DCoordinates: (-4,-1),(-1,1),(2,-1),(5,-3),(8,-1)Find the amplitude, period, phase shift, domain, and range. **Problem Set: Identifying Properties of Trigonometric Functions**### Instructions:For problems 8, 9, and 10, identify the amplitude (if appropriate), period, phase shift, domain, and range. Then, write a function in the indicated form for the given graph. If you cannot see the coordinates clearly, zoom in on the graph.---#### Problem 8Given: $ f(x) = A \sin(Bx - C) + D $**Graph Analysis:**- Coordinates on the graph: - Peak at $(-1, 1)$ - Valley at $(5, -3)$ - Crosses the x-axis at $(-4, 0)$, $(2, 1)$, and $(8, -1)$**Questions:**- **Amplitude:**- **Period:**- **Phase Shift:**- **Domain:**- **Range:**#### Graph Description:The graph displayed is a sinusoidal curve. Notable points include $(-1, 1)$ as the maximum, and $(5, -3)$ as the minimum. These points help determine the amplitude and vertical shift. The curve crosses the x-axis at $(-4, 0)$, $(2, 1)$, and $(8, -1)$, which helps identify the period and phase shift.---#### Problem 9Given: $ f(x) = A \tan(Bx - C) + D $**Questions:**- **Amplitude:**- **Period:**- **Phase Shift:**- **Domain:**- **Range:***(Graph and information for this problem are not provided here, so make sure to refer to your material.)*---Please use the given dimensions and points to solve for each parameter accurately. Analyze the graphs provided, understanding their periodic nature and how their properties correspond to the general forms of trigonometric functions.

Carefully observe, the plot for the f (x). The horizontal line y = -1 is the mid line for the…

Answered: 8. f(x) = A sin(Bx – C) + D %3D…

Math

Trigonometry

8. f(x) = A sin(Bx – C) + D %3D amplitude: period: (-1.1) (2.+1) (8-1) phase shift: (4-1) (5.-3) domain: range:

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

f(x)=Asin(Bx-C)+D

Coordinates: (-4,-1),(-1,1),(2,-1),(5,-3),(8,-1)

Find the amplitude, period, phase shift, domain, and range.

**Problem Set: Identifying Properties of Trigonometric Functions**

### Instructions:
For problems 8, 9, and 10, identify the amplitude (if appropriate), period, phase shift, domain, and range. Then, write a function in the indicated form for the given graph. If you cannot see the coordinates clearly, zoom in on the graph.

---

#### Problem 8
Given: $ f(x) = A \sin(Bx - C) + D $

**Graph Analysis:**
- Coordinates on the graph:
- Peak at $(-1, 1)$
- Valley at $(5, -3)$
- Crosses the x-axis at $(-4, 0)$, $(2, 1)$, and $(8, -1)$

**Questions:**
- **Amplitude:**
- **Period:**
- **Phase Shift:**
- **Domain:**
- **Range:**

#### Graph Description:
The graph displayed is a sinusoidal curve. Notable points include $(-1, 1)$ as the maximum, and $(5, -3)$ as the minimum. These points help determine the amplitude and vertical shift. The curve crosses the x-axis at $(-4, 0)$, $(2, 1)$, and $(8, -1)$, which helps identify the period and phase shift.

---

#### Problem 9
Given: $ f(x) = A \tan(Bx - C) + D $

**Questions:**
- **Amplitude:**
- **Period:**
- **Phase Shift:**
- **Domain:**
- **Range:**

*(Graph and information for this problem are not provided here, so make sure to refer to your material.)*

---

Please use the given dimensions and points to solve for each parameter accurately. Analyze the graphs provided, understanding their periodic nature and how their properties correspond to the general forms of trigonometric functions.

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