y=p(x)} Ty=h(x) 11 10 6. 5 y=g(x) y=f(x) 3. 2.

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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  1. Define the function p using the function f.
  2. What is the function rule for p?
The image illustrates a graph with three quadratic functions plotted on a Cartesian coordinate grid.

1. **Function \( f(x) \)**:
   - Depicted in black.
   - Has a vertex at \((0, 1)\) and opens upwards.
   - Symmetrical about the y-axis.
   - Passes through points such as \((-3, 10)\), \((-2, 5)\), \((-1, 2)\), \((1, 2)\), \((2, 5)\), \((3, 10)\).

2. **Function \( g(x) \)**:
   - Shown in blue.
   - Opens upwards with a vertex at \((5, 0)\).
   - Symmetrical about the line \(x = 5\).
   - Passes through points such as \((3, 4)\), \((4, 1)\), \((6, 1)\), \((7, 4)\).

3. **Function \( h(x) \)** and **Function \( p(x) \)**:
   - Function \( h(x) \) is in red, and Function \( p(x) \) is in green.
   - Both have vertices close to \((4, 0)\) and open upwards.
   - They trace closely but are not identical, with \( h(x) \) slightly broader than \( p(x) \).
   - The vertex of \( h(x) \) is at \((4,1)\) and it runs above \( p(x)\).

The grid lines indicate integer values on the x-axis from \(-3\) to \(8\) and on the y-axis from \(1\) to \(11\). The functions illustrate different parabolic shapes and transformations compared to the basic function \( f(x) \).
Transcribed Image Text:The image illustrates a graph with three quadratic functions plotted on a Cartesian coordinate grid. 1. **Function \( f(x) \)**: - Depicted in black. - Has a vertex at \((0, 1)\) and opens upwards. - Symmetrical about the y-axis. - Passes through points such as \((-3, 10)\), \((-2, 5)\), \((-1, 2)\), \((1, 2)\), \((2, 5)\), \((3, 10)\). 2. **Function \( g(x) \)**: - Shown in blue. - Opens upwards with a vertex at \((5, 0)\). - Symmetrical about the line \(x = 5\). - Passes through points such as \((3, 4)\), \((4, 1)\), \((6, 1)\), \((7, 4)\). 3. **Function \( h(x) \)** and **Function \( p(x) \)**: - Function \( h(x) \) is in red, and Function \( p(x) \) is in green. - Both have vertices close to \((4, 0)\) and open upwards. - They trace closely but are not identical, with \( h(x) \) slightly broader than \( p(x) \). - The vertex of \( h(x) \) is at \((4,1)\) and it runs above \( p(x)\). The grid lines indicate integer values on the x-axis from \(-3\) to \(8\) and on the y-axis from \(1\) to \(11\). The functions illustrate different parabolic shapes and transformations compared to the basic function \( f(x) \).
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