13. Given the graphs of f(x), g(x) and h(x), determine: -3 -2 -1 =h(x) a) f(3) d) h(g(1)) -2 -1 10 y = f(x) АЛА 1 b) (h-f)(5) e) (foh)(-3) c) (fx h) (0) f) (g° g)(3)
13. Given the graphs of f(x), g(x) and h(x), determine: -3 -2 -1 =h(x) a) f(3) d) h(g(1)) -2 -1 10 y = f(x) АЛА 1 b) (h-f)(5) e) (foh)(-3) c) (fx h) (0) f) (g° g)(3)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Kk 159.
![### Problem 13: Analysis of Given Graphs
Given the graphs of the functions \( f(x) \), \( g(x) \), and \( h(x) \), determine the following:
1. \( f(3) \)
2. \( (h-f)(5) \)
3. \( (f \times h)(0) \)
4. \( h(g(1)) \)
5. \( (f \circ h)(-3) \)
6. \( (g \circ g)(3) \)
7. \( (f \circ h)(0) \)
8. \( h(g(f(-5))) \)
#### Explanation of Graphs:
1. **Graph of \( f(x) \):**
- Shape: Parabola opening upwards.
- Domain: Extends beyond \([-5, 5]\).
- Range: \([-6, 4]\).
- Points: Passes through \((0, -6)\), \((-3, 3)\), and \((3, 3)\).
2. **Graph of \( g(x) \):**
- Shape: Sinusoidal wave.
- Domain: Extends beyond \([-5, 5]\).
- Range: \([-6, 6]\).
- Periodicity: Repeats every \(2\pi\) units approximately.
3. **Graph of \( h(x) \):**
- Shape: V-shaped absolute value function flipped and shifted.
- Domain: Extends beyond \([-5, 5]\).
- Range: \([-5, 5]\).
- Points: Passes through \((0, 5)\), \((5, 0)\), \((-5, 0)\).
#### Tasks:
a) \( f(3) \)
b) \( (h - f)(5) \)
c) \( (f \times h)(0) \)
d) \( h(g(1)) \)
e) \( (f \circ h)(-3) \)
f) \( (g \circ g)(3) \)
g) \( (f \circ h)(0) \)
h) \( h(g(f(-5))) \)
**Note:** Symbols like \( \circ \) represent function composition (e.g., \( (f \circ h)(x) = f(h(x))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F816cc47c-f059-4914-940d-8196a7c7af6b%2Ff22b7f94-3526-4878-af5a-b90b724c6b8e%2Fuygtu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 13: Analysis of Given Graphs
Given the graphs of the functions \( f(x) \), \( g(x) \), and \( h(x) \), determine the following:
1. \( f(3) \)
2. \( (h-f)(5) \)
3. \( (f \times h)(0) \)
4. \( h(g(1)) \)
5. \( (f \circ h)(-3) \)
6. \( (g \circ g)(3) \)
7. \( (f \circ h)(0) \)
8. \( h(g(f(-5))) \)
#### Explanation of Graphs:
1. **Graph of \( f(x) \):**
- Shape: Parabola opening upwards.
- Domain: Extends beyond \([-5, 5]\).
- Range: \([-6, 4]\).
- Points: Passes through \((0, -6)\), \((-3, 3)\), and \((3, 3)\).
2. **Graph of \( g(x) \):**
- Shape: Sinusoidal wave.
- Domain: Extends beyond \([-5, 5]\).
- Range: \([-6, 6]\).
- Periodicity: Repeats every \(2\pi\) units approximately.
3. **Graph of \( h(x) \):**
- Shape: V-shaped absolute value function flipped and shifted.
- Domain: Extends beyond \([-5, 5]\).
- Range: \([-5, 5]\).
- Points: Passes through \((0, 5)\), \((5, 0)\), \((-5, 0)\).
#### Tasks:
a) \( f(3) \)
b) \( (h - f)(5) \)
c) \( (f \times h)(0) \)
d) \( h(g(1)) \)
e) \( (f \circ h)(-3) \)
f) \( (g \circ g)(3) \)
g) \( (f \circ h)(0) \)
h) \( h(g(f(-5))) \)
**Note:** Symbols like \( \circ \) represent function composition (e.g., \( (f \circ h)(x) = f(h(x))
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