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Domain of a Function Identify the Domain of the following functions. Write your answers in Interval Notation. Domain Function p(t) = -3t-6 f(x) = 5x² - 1 1 x + 7 h(x)=√x-8 g(x) =

Domain of a Function Identify the Domain of the following functions. Write your answers in Interval Notation. Domain Function p(t) = -3t-6 f(x) = 5x² - 1 1 x + 7 h(x)=√x-8 g(x) =

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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### Domain of a Function **Identify the Domain of the following functions. Write your answers in Interval Notation.** | Function | Domain | |-----------------------------------------|------------------------| | \( p(t) = -3t - 6 \) | | | \( f(x) = 5x^2 - 1 \) | | | \( g(x) = \frac{1}{x + 7} \) | | | \( h(x) = \sqrt{x - 8} \) | | To find the domains of the given functions, we consider the restrictions on the input values \( t \) and \( x \): 1. **For \( p(t) = -3t - 6 \):** - This is a linear function. - A linear function is defined for all real numbers. - **Domain:** \( (-\infty, \infty) \) 2. **For \( f(x) = 5x^2 - 1 \):** - This is a polynomial function. - Polynomial functions are defined for all real numbers. - **Domain:** \( (-\infty, \infty) \) 3. **For \( g(x) = \frac{1}{x + 7} \):** - This is a rational function. - A rational function is defined everywhere except where the denominator is zero. - To find the restriction, solve \( x + 7 = 0 \). - \( x = -7 \) - **Domain:** \( (-\infty, -7) \cup (-7, \infty) \) 4. **For \( h(x) = \sqrt{x - 8} \):** - This is a square root function. - A square root function is defined for all values of \( x \) for which the expression under the square root is non-negative. - Solve \( x - 8 \geq 0 \). - \( x \geq 8 \) - **Domain:** \( [8, \infty) \) Thus, the completed table should look like this: | Function | Domain | |-----------------------------------------|------------------------------------| | \( p(t) = -3t - 6 \) | \( (-\infty, \infty) \)
Transcribed Image Text:### Domain of a Function **Identify the Domain of the following functions. Write your answers in Interval Notation.** | Function | Domain | |-----------------------------------------|------------------------| | \( p(t) = -3t - 6 \) | | | \( f(x) = 5x^2 - 1 \) | | | \( g(x) = \frac{1}{x + 7} \) | | | \( h(x) = \sqrt{x - 8} \) | | To find the domains of the given functions, we consider the restrictions on the input values \( t \) and \( x \): 1. **For \( p(t) = -3t - 6 \):** - This is a linear function. - A linear function is defined for all real numbers. - **Domain:** \( (-\infty, \infty) \) 2. **For \( f(x) = 5x^2 - 1 \):** - This is a polynomial function. - Polynomial functions are defined for all real numbers. - **Domain:** \( (-\infty, \infty) \) 3. **For \( g(x) = \frac{1}{x + 7} \):** - This is a rational function. - A rational function is defined everywhere except where the denominator is zero. - To find the restriction, solve \( x + 7 = 0 \). - \( x = -7 \) - **Domain:** \( (-\infty, -7) \cup (-7, \infty) \) 4. **For \( h(x) = \sqrt{x - 8} \):** - This is a square root function. - A square root function is defined for all values of \( x \) for which the expression under the square root is non-negative. - Solve \( x - 8 \geq 0 \). - \( x \geq 8 \) - **Domain:** \( [8, \infty) \) Thus, the completed table should look like this: | Function | Domain | |-----------------------------------------|------------------------------------| | \( p(t) = -3t - 6 \) | \( (-\infty, \infty) \)
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