Question

One solid and one dotted curve are drawn in a coordinate plane. The x-axis ranges from negative 2 to 2 and the y-axis ranges from negative 2 to 3, both by 1-unit increments.
Compare the graphs of f(x)=2x+1−−−−√
and g(x)=2x+1−−−−√3
. What is the y-intercept of both graphs?

(1 point)
They both have a y-intercept at (0,
).

Answer 1

To find the y-intercepts of the functions \( f(x) = \sqrt{2x + 1} \) and \( g(x) = \frac{\sqrt{2x + 1}}{3} \), we need to evaluate each function at \( x = 0 \).

**For \( f(x) \):**
\[
f(0) = \sqrt{2(0) + 1} = \sqrt{1} = 1
\]

**For \( g(x) \):**
\[
g(0) = \frac{\sqrt{2(0) + 1}}{3} = \frac{\sqrt{1}}{3} = \frac{1}{3}
\]

So the y-intercepts are:
- For \( f(x) \): \( (0, 1) \)
- For \( g(x) \): \( (0, \frac{1}{3}) \)

Therefore, they both have a y-intercept at:
\[
(0, \text{at } 1) \text{ and } (0, \text{at } \frac{1}{3})
\]

To complete the sentence:
They both have a y-intercept at \( (0, 1) \) for \( f(x) \) and \( (0, \frac{1}{3}) \) for \( g(x) \).