Use the image to answer the question.

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-intercept of both graphs \( f(x) = \sqrt{2x + 1} \) 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 \( g(x) \):

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

Thus, we have:

• The y-intercept of \( f(x) \) is \( (0, 1) \).
• The y-intercept of \( g(x) \) is \( (0, \frac{1}{3}) \).

Therefore, both graphs have a y-intercept at \( (0, y) \) where \( y = 1 \) for \( f(x) \) and \( y = \frac{1}{3} \) for \( g(x) \).