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g(x) = x³ + x? - 8x- 12 f(x) = x² + 4x +3 %3D h(x) = x² + 3 %3D s(x) = x² - 3x

g(x) = x³ + x? - 8x- 12 f(x) = x² + 4x +3 %3D h(x) = x² + 3 %3D s(x) = x² - 3x

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
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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Place each statement next to the correct function

### Identifying Characteristics of Functions **Instructions:** Place each statement next to the correct function. **Statements:** 1. Function has zeros of multiplicity. 2. (x + 3) is a factor of this function. 3. Zero is an x-intercept for the graph of this function. 4. One is an x-intercept for the graph of this function. 5. Solution set for this function is {3, -3}. 6. Function has nonreal solutions.
Transcribed Image Text:### Identifying Characteristics of Functions **Instructions:** Place each statement next to the correct function. **Statements:** 1. Function has zeros of multiplicity. 2. (x + 3) is a factor of this function. 3. Zero is an x-intercept for the graph of this function. 4. One is an x-intercept for the graph of this function. 5. Solution set for this function is {3, -3}. 6. Function has nonreal solutions.
### Polynomial Functions In mathematics, a polynomial function is a function that can be expressed in terms of a polynomial. Here are some examples of polynomial functions, represented with their equations: 1. **Function \( g(x) \):** \[ g(x) = x^3 + x^2 - 8x - 12 \] This is a cubic polynomial function because the highest exponent of \( x \) is 3. 2. **Function \( f(x) \):** \[ f(x) = x^2 + 4x + 3 \] This is a quadratic polynomial function because the highest exponent of \( x \) is 2. 3. **Function \( h(x) \):** \[ h(x) = x^2 + 3 \] This is another example of a quadratic polynomial function. 4. **Function \( s(x) \):** \[ s(x) = x^2 - 3x \] This is also a quadratic polynomial function. Each of these polynomial functions can be graphed on a coordinate plane. The shape of the graph will depend on the degree of the polynomial and the coefficients in the equation. #### Graphical Interpretation (Not Provided in Image) - A cubic function (\( g(x) \)) will have a graph that can change direction up to two times and has the potential to have three real or complex roots. - A quadratic function (\( f(x) \), \( h(x) \), and \( s(x) \)) will have a parabolic shape, opening upward if the coefficient of \( x^2 \) is positive and downward if it is negative. Understanding these functions and their graphs is key in algebra and calculus for solving equations and inequalities.
Transcribed Image Text:### Polynomial Functions In mathematics, a polynomial function is a function that can be expressed in terms of a polynomial. Here are some examples of polynomial functions, represented with their equations: 1. **Function \( g(x) \):** \[ g(x) = x^3 + x^2 - 8x - 12 \] This is a cubic polynomial function because the highest exponent of \( x \) is 3. 2. **Function \( f(x) \):** \[ f(x) = x^2 + 4x + 3 \] This is a quadratic polynomial function because the highest exponent of \( x \) is 2. 3. **Function \( h(x) \):** \[ h(x) = x^2 + 3 \] This is another example of a quadratic polynomial function. 4. **Function \( s(x) \):** \[ s(x) = x^2 - 3x \] This is also a quadratic polynomial function. Each of these polynomial functions can be graphed on a coordinate plane. The shape of the graph will depend on the degree of the polynomial and the coefficients in the equation. #### Graphical Interpretation (Not Provided in Image) - A cubic function (\( g(x) \)) will have a graph that can change direction up to two times and has the potential to have three real or complex roots. - A quadratic function (\( f(x) \), \( h(x) \), and \( s(x) \)) will have a parabolic shape, opening upward if the coefficient of \( x^2 \) is positive and downward if it is negative. Understanding these functions and their graphs is key in algebra and calculus for solving equations and inequalities.
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