Sketch the graph of the associated function, $g ( x ) = - | x |$ then draw the graph of the function f using a translation and/or a reflection, and give its domain and range. $f ( x ) = - | x | + 2$
A) D= the set of all real numbers greater than or equal to 2 R= the set of all real numbers
B) D= the set of all real numbers R= the set of all real numbers less than or equal to 2
C) D= the set of all real numbers less than or equal to 2 R= the set of all real numbers
D) D= the set of all real numbers greater than or equal to 2 R= the set of all real numbers less than or equal to 2
E) D= the set of all real numbers R= the set of all real numbers greater than or equal to 2

Question

Sketch the graph of the associated function, $g ( x ) = - | x |$ then draw the graph of the function f using a translation and/or a reflection, and give its domain and range. $f ( x ) = - | x | + 2$
A) D= the set of all real numbers greater than or equal to 2 R= the set of all real numbers
B) D=  the set of all real numbers R= the set of all real numbers less than or equal to 2
C) D= the set of all real numbers less than or equal to 2 R= the set of all real numbers
D) D= the set of all real numbers greater than or equal to 2 R=  the set of all real numbers less than or equal to 2
E) D= the set of all real numbers R= the set of all real numbers greater than or equal to 2

Quizplus · Accepted Answer

The function $f(x) = -|x| + 2$ is a translation of $g(x) = -|x|$ upwards by 2 units. The domain of $f(x)$ remains all real numbers since the translation does not affect the x-values over which the function is defined. The range is all real numbers less than or equal to 2 because the vertex of the V-shaped graph of $g(x)$ is translated from (0,0) to (0,2), and since $g(x)$ is always less than or equal to 0, $f(x)$ is always less than or equal to 2.

Sketch the Graph of the Associated Function g(x)=−∣x∣g ( x ) = - | x |g(x)=−∣x∣

Sketch the Graph of the Associated Function $g ( x ) = - | x |$