To determine the [tex]\(y\)[/tex]-intercept of the function [tex]\(f(x) = \left(\frac{1}{4}\right)^x\)[/tex], we follow these steps:
1. Understand the concept of [tex]\(y\)[/tex]-intercept:
- The [tex]\(y\)[/tex]-intercept is the point where the graph of the function intersects the [tex]\(y\)[/tex]-axis.
- At this point, the value of [tex]\(x\)[/tex] is always 0.
2. Substitute [tex]\(x = 0\)[/tex] into the function:
- We substitute [tex]\(x = 0\)[/tex] in the function [tex]\(f(x) = \left(\frac{1}{4}\right)^x\)[/tex].
3. Evaluate the function at [tex]\(x = 0\)[/tex]:
[tex]\[
f(0) = \left(\frac{1}{4}\right)^0
\][/tex]
- Any non-zero number raised to the power of 0 equals 1.
[tex]\[
\left(\frac{1}{4}\right)^0 = 1
\][/tex]
4. Determine the [tex]\(y\)[/tex]-intercept as a coordinate point:
- The [tex]\(y\)[/tex]-intercept is therefore the point [tex]\((0, 1)\)[/tex].
Given the choices:
- A. [tex]\((0, 1)\)[/tex]
- B. [tex]\(\left(1, \frac{1}{4}\right)\)[/tex]
- C. [tex]\((0, 0)\)[/tex]
- D. [tex]\((1, 0)\)[/tex]
The correct answer is:
A. [tex]\((0, 1)\)[/tex]
