Question
Compare the graphs of f(x)=2x+1−−−−−√ and g(x)=2^3√x+1−−−−− . What is the y-intercept of both graphs?
Answers
GPT-4o mini
To compare the graphs of the functions \( f(x) = \sqrt{2x + 1} \) and \( g(x) = \sqrt[3]{2x + 1} \), we can start with finding their y-intercepts.
The y-intercept of a function is found by evaluating the function at \( x = 0 \).
1. **Finding the y-intercept of \( f(x) \)**:
\[
f(0) = \sqrt{2(0) + 1} = \sqrt{1} = 1
\]
So, the y-intercept of \( f(x) \) is \( (0, 1) \).
2. **Finding the y-intercept of \( g(x) \)**:
\[
g(0) = \sqrt[3]{2(0) + 1} = \sqrt[3]{1} = 1
\]
So, the y-intercept of \( g(x) \) is also \( (0, 1) \).
In conclusion, both functions \( f(x) \) and \( g(x) \) have the same y-intercept, which is \( (0, 1) \).
The y-intercept of a function is found by evaluating the function at \( x = 0 \).
1. **Finding the y-intercept of \( f(x) \)**:
\[
f(0) = \sqrt{2(0) + 1} = \sqrt{1} = 1
\]
So, the y-intercept of \( f(x) \) is \( (0, 1) \).
2. **Finding the y-intercept of \( g(x) \)**:
\[
g(0) = \sqrt[3]{2(0) + 1} = \sqrt[3]{1} = 1
\]
So, the y-intercept of \( g(x) \) is also \( (0, 1) \).
In conclusion, both functions \( f(x) \) and \( g(x) \) have the same y-intercept, which is \( (0, 1) \).