Question

use your graphing calculator to sketch the graph of the following quadratic function, then determine the domain and range.
( g(x) = -x^2 + 9x - 8 )

sketch the graph of the function in the viewing window ( -10, 10 \times -15, 15 ). choose the correct graph below.
a. b. c. d.
graphs are shown with magnifying and other icons

determine the domain of the function. select the correct choice below and fill in any answer boxes within your choice
a. the domain is
(type an inequality or a compound inequality.)
b. the domain is all real numbers.

Explanation:

Step1: Recall the definition of domain

The domain of a function is the set of all possible input values (x - values) for which the function is defined.

Step2: Analyze the function \( g(x)=-x^{2}+9x - 8 \)

This is a quadratic function, which is a polynomial function. Polynomial functions (including linear, quadratic, cubic, etc.) are defined for all real numbers because there are no restrictions on the values of \( x \) that would make the function undefined (such as division by zero or taking the square root of a negative number, which are restrictions in other types of functions like rational or square - root functions). So, for the quadratic function \( g(x)=-x^{2}+9x - 8 \), there are no values of \( x \) for which \( g(x) \) is not defined. Thus, the domain of the function is all real numbers.

Answer:

B. The domain is all real numbers.