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Use the image to answer the 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,
).
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1 answer

To find the y-intercepts of the functions \( f(x) = \sqrt{2x + 1} \) and \( g(x) = \frac{\sqrt{2x + 1}}{3} \), we substitute \( x = 0 \) into both equations.

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

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

Thus, the y-intercepts are:

  • For \( f(x) \): \( (0, 1) \)
  • For \( g(x) \): \( (0, \frac{1}{3}) \)

Therefore, they both have y-intercepts at:

  • \( (0, 1) \) for \( f(x) \)
  • \( (0, \frac{1}{3}) \) for \( g(x) \)

So, the answer to the question is:

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