Can you help me finish these homework questions? **Characteristics of Polynomial and Rational Functions****Left Side:****Graph of the function f(x) = 9 - (x - 4)²:**- The graph is a downward-opening parabola with its peak at a single point, indicating the vertex.**Vertex:**- Ordered Pair: (4, 9)**Axis of Symmetry:**- Equation of the Line: $ y = 4 $**Intercepts:**- **x-intercepts:** - Ordered Pairs: (7, 0) & (1, 0) - **y-intercepts:** - Ordered Pair: (0, 7)**Domain:**- Interval Notation: (-∞, ∞)**Range:**- Interval Notation: (-∞, ∞)**Maximum Values:**- Where does $ f $ have a local/relative maximum? - At x = 4- What is the local/relative maximum value? - 9**Right Side:****Graph of the function f(x) = x² + 6x + 5:**- The graph is an upward-opening parabola.**Vertex:**- Ordered Pair: (Not provided, requires calculation by completing the square or using the formula $ x = -\frac{b}{2a} $)**Axis of Symmetry:**- Equation of the Line: (To be calculated)**Intercepts:**- **x-intercepts:** - Ordered Pairs: (To be calculated using the quadratic formula or factoring) - **y-intercepts:** - Ordered Pair: (Not provided, typically x = 0 and solve for y)**Domain:**- Interval Notation: (-∞, ∞)**Range:**- Interval Notation: (To be determined based on the vertex)**Minimum Values:**- Where does $ f $ have a local/relative minimum? - (To be determined) - What is the local/relative minimum value? - (To be determined)These characteristics help in understanding the behavior of polynomial functions through their graphs, intercepts, and extremum points.

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Description: Can you help me finish these homework questions? **Characteristics of Polynomial and Rational Functions****Left Side:****Graph of the function f(x) = 9 - (x - 4)²:**- The graph is a downward-opening parabola with its peak at a single point, indicatin

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Answered: 10 -10 8 to 10 f(x) = 9– (x – 4)²…

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10 -10 8 to 10 f(x) = 9– (x – 4)² Vertex ordered pair dod bn to o -8 Axis of symmetry = y= Equation of the line (7,0) . (1,0) x - intercepts_ & ordered pairs

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 7E

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Can you help me finish these homework questions?

**Characteristics of Polynomial and Rational Functions**

**Left Side:**

**Graph of the function f(x) = 9 - (x - 4)²:**

- The graph is a downward-opening parabola with its peak at a single point, indicating the vertex.

**Vertex:**

- Ordered Pair: (4, 9)

**Axis of Symmetry:**

- Equation of the Line: $ y = 4 $

**Intercepts:**

- **x-intercepts:**
- Ordered Pairs: (7, 0) & (1, 0)

- **y-intercepts:**
- Ordered Pair: (0, 7)

**Domain:**

- Interval Notation: (-∞, ∞)

**Range:**

- Interval Notation: (-∞, ∞)

**Maximum Values:**

- Where does $ f $ have a local/relative maximum?
- At x = 4
- What is the local/relative maximum value?
- 9

**Right Side:**

**Graph of the function f(x) = x² + 6x + 5:**

- The graph is an upward-opening parabola.

**Vertex:**

- Ordered Pair: (Not provided, requires calculation by completing the square or using the formula $ x = -\frac{b}{2a} $)

**Axis of Symmetry:**

- Equation of the Line: (To be calculated)

**Intercepts:**

- **x-intercepts:**
- Ordered Pairs: (To be calculated using the quadratic formula or factoring)

- **y-intercepts:**
- Ordered Pair: (Not provided, typically x = 0 and solve for y)

**Domain:**

- Interval Notation: (-∞, ∞)

**Range:**

- Interval Notation: (To be determined based on the vertex)

**Minimum Values:**

- Where does $ f $ have a local/relative minimum?
- (To be determined)

- What is the local/relative minimum value?
- (To be determined)

These characteristics help in understanding the behavior of polynomial functions through their graphs, intercepts, and extremum points.

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