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Question 1 (5 points)

Given [tex]\( f(x) = 5^{2x} \)[/tex], evaluate [tex]\( f(-1) \)[/tex], [tex]\( f(0) \)[/tex], and [tex]\( f(2) \)[/tex].

A. [tex]\( 25, 1, -25 \)[/tex]

B. [tex]\( \frac{1}{25}, 0, 625 \)[/tex]

C. [tex]\( \frac{1}{25}, 1, 625 \)[/tex]

D. [tex]\( \frac{1}{25}, 0, 25 \)[/tex]



Answer :

GinnyAnswer
Sure, let's evaluate the function [tex]\( f(x) = 5^{2x} \)[/tex] at the given points one by one.

### Step 1: Evaluating [tex]\( f(-1) \)[/tex]

For [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = 5^{2 \cdot (-1)} = 5^{-2} \][/tex]

By the rules of exponents, [tex]\( 5^{-2} \)[/tex] is equivalent to [tex]\( \frac{1}{5^2} \)[/tex]:
[tex]\[ f(-1) = \frac{1}{25} \][/tex]

### Step 2: Evaluating [tex]\( f(0) \)[/tex]

For [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 5^{2 \cdot 0} = 5^0 \][/tex]

Any non-zero number raised to the power of 0 is 1:
[tex]\[ f(0) = 1 \][/tex]

### Step 3: Evaluating [tex]\( f(2) \)[/tex]

For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 5^{2 \cdot 2} = 5^4 \][/tex]

Calculating [tex]\( 5^4 \)[/tex]:
[tex]\[ 5^4 = 625 \][/tex]

### Conclusion

After evaluating the function at the given points, we have:
- [tex]\( f(-1) = \frac{1}{25} \)[/tex]
- [tex]\( f(0) = 1 \)[/tex]
- [tex]\( f(2) = 625 \)[/tex]

Thus, the correct evaluation gives us:
[tex]\[ f(-1) = \frac{1}{25}, \; f(0) = 1, \; f(2) = 625 \][/tex]

Therefore, the correct choice is:
[tex]\[ \boxed{\frac{1}{25}, \; 1, \; 625} \][/tex]

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