Question

use your graphing calculator to sketch the graph of the following quadratic function, then determine the domain and range.

$y = -x^2 + 7$

sketch the graph of the function $y = -x^2 + 7$. choose the correct graph below.

\\(\bigcirc\\) a. \\(\bigcirc\\) b. \\(\bigcirc\\) c. \\(\bigcirc\\) d.

-12, 12, 4 by -12, 12, 4

determine the domain of the function. select the correct choice below and fill in any answer boxes within your choice.

\\(\bigcirc\\) a. the domain is \\(
\\) (type an inequality or a compound inequality.)
\\(\bigcirc\\) 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 \( y = -x^{2}+7 \)

This is a quadratic function, which is a polynomial function. Polynomial functions (including quadratic functions) are defined for all real numbers because there are no restrictions on the values of \( x \) (such as division by zero or taking the square root of a negative number) in the expression \( -x^{2}+7 \). For any real number \( x \), we can compute \( -x^{2}+7 \) by squaring \( x \), multiplying by - 1, and then adding 7. So the domain of the function \( y=-x^{2} + 7\) is all real numbers.

Answer:

B. The domain is all real numbers.