Graph the function by plotting the points and give its domain and range. $f ( x ) = - x ^ { 2 } + 1$
A) D= the set of all real numbers less than or equal to 1 R= the set of all real numbers
B) D= the set of all real numbers R= the set of all real numbers greater than or equal to 1
C) D= the set of all real numbers greater than or equal to 1 R= the set of all real numbers less than or equal to 1
D) D= the set of all real numbers $R =$ the set of all real numbers less than or equal to $1$
E) $D =$ the set of all real numbers greater than or equal to $1$ $R =$ the set of all real numbers

Question

Graph the function by plotting the points and give its domain and range. $f ( x ) = - x ^ { 2 } + 1$
A) D= the set of all real numbers less than or equal to 1 R= the set of all real numbers
B) D=  the set of all real numbers R= the set of all real numbers greater than or equal to 1
C) D= the set of all real numbers greater than or equal to 1  R= the set of all real numbers less than or equal to 1
D) D=  the set of all real numbers $R =$ the set of all real numbers less than or equal to $1$
E) $D =$ the set of all real numbers greater than or equal to $1$ $R =$ the set of all real numbers

Quizplus · Accepted Answer

The function is of the form of a downward facing parabola. The highest point of the parabola is at (0,1) and it extends downward towards negative infinity. Therefore, the domain is all real numbers and the range is all real numbers less than or equal to 1, which matches option D.

Graph the Function by Plotting the Points and Give Its f(x)=−x2+1f ( x ) = - x ^ { 2 } + 1f(x)=−x2+1

Graph the Function by Plotting the Points and Give Its $f ( x ) = - x ^ { 2 } + 1$