does the function $y = \\frac{1}{x^{2}}$ shown in the graph below have a maximum y - value or a minimum y…
does the function $y = \\frac{1}{x^{2}}$ shown in the graph below have a maximum y - value or a minimum y - value?\na. cannot be determined\nc. no\nb. yes, maximum value is 5 and minimum\nd. yes, maximum value is 100 and minimum\nvalue is 0\nvalue is - 100
Answer
Answer:
C. No
Explanation:
Step 1: Analyze the function ( y = \frac{1}{x^2} )
The function is always positive since ( x^2 > 0 ) for all ( x \neq 0 ).
Step 2: Examine behavior as ( x \to 0 )
As ( x ) approaches 0, ( y ) increases without bound (no maximum).
Step 3: Examine behavior as ( x \to \pm\infty )
As ( x ) approaches infinity, ( y ) approaches 0 but never reaches it (no minimum value is attained).
Step 4: Evaluate options
Options B and D incorrectly specify finite max/min values. The function has no defined maximum or minimum, so the answer is C.