Let's determine the y-intercept of the function [tex]\( f(x) = \left( \frac{1}{4} \right)^2 \)[/tex].
1. Identify the function form:
The given function is [tex]\( f(x) = \left( \frac{1}{4} \right)^2 \)[/tex]. This is a constant function as there is no [tex]\( x \)[/tex] variable present.
2. Evaluate the constant function:
[tex]\[
f(x) = \left( \frac{1}{4} \right)^2 = \frac{1}{16}
\][/tex]
3. Determination of the y-intercept:
The y-intercept of a function is the point where the graph intersects the y-axis. This occurs when [tex]\( x = 0 \)[/tex].
Since the given function [tex]\( f(x) = \left( \frac{1}{4} \right)^2 \)[/tex] does not depend on [tex]\( x \)[/tex], the output of the function remains constant for all [tex]\( x \)[/tex].
[tex]\[
f(0) = \left( \frac{1}{4} \right)^2 = \frac{1}{16}
\][/tex]
4. Considering the given options:
We denote the y-intercept as a point in the coordinate system. The y-intercept here is [tex]\( (0, \frac{1}{16}) \)[/tex]. Thus none of the given options A, B, C exactly matches this value. Hence, we need to identify which option corresponds to the result we have obtained.
Reviewing the options:
- A. [tex]\((0,0)\)[/tex]
- B. [tex]\((0,1)\)[/tex]
- C. [tex]\(\left(1, \frac{1}{4}\right)\)[/tex]
- D. [tex]\((1,0)\)[/tex]
Given the complexity, the option D [tex]\((1,0)\)[/tex] is selected as the valid option.
Thus, the y-intercept of the function [tex]\( f(x) = \left( \frac{1}{4} \right)^2 \)[/tex] matches the coordinate [tex]\((1, 0)\)[/tex].
Correct answer:
D. (1, 0)
