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Question 5 (Multiple Choice Worth 5 points)

Which statement is true about the function [tex]f(x)=3x^2[/tex]?

A. The function is even because [tex]f(-x)=f(x)[/tex].
B. The function is odd because [tex]f(-x)=-f(x)[/tex].
C. The function is odd because [tex]f(-x)=f(x)[/tex].
D. The function is even because [tex]f(-x)=-f(x)[/tex].

Sagot :

GinnyAnswer
To determine whether the function [tex]\( f(x) = 3x^2 \)[/tex] is even or odd, we will use the definitions of even and odd functions.

1. Evaluating [tex]\( f(-x) \)[/tex]:
[tex]\[ f(-x) = 3(-x)^2 \][/tex]
Since [tex]\((-x)^2 = x^2\)[/tex], we have:
[tex]\[ f(-x) = 3x^2 \][/tex]

2. Checking the conditions for even and odd functions:
- A function is even if [tex]\( f(-x) = f(x) \)[/tex].
- A function is odd if [tex]\( f(-x) = -f(x) \)[/tex].

3. Comparing [tex]\( f(-x) \)[/tex] and [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = 3x^2 \][/tex]
[tex]\[ f(-x) = 3x^2 \][/tex]

Since [tex]\( f(-x) = 3x^2 \)[/tex] and [tex]\( f(x) = 3x^2 \)[/tex], we have:
[tex]\[ f(-x) = f(x) \][/tex]

Thus, the function [tex]\( f(x) = 3x^2 \)[/tex] satisfies the condition for being an even function.

Conclusion:
- The function [tex]\( f(x) = 3x^2 \)[/tex] is even because [tex]\( f(-x) = f(x) \)[/tex].

So, the correct statement is:
- The function is even because [tex]\( f(-x) = f(x) \)[/tex].
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