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Consider the graph of the function \( f(x) = 2^x \). Which statements describe key features of function \(...

Select all the correct answers.
Consider the graph of the function \( f(x) = 2^x \).
Which statements describe key features of function \( g \) if \( g(x) = f(x + 2) \) ?
□ horizontal asymptote of \( y = 0 \)
□ \( y \)-intercept at \( (0, 1) \)
□ horizontal asymptote of \( y = 2 \)
□ \( y \)-intercept at \( (0, 4) \)
□ domain of \( \{x| -\infty < x < \infty\} \)

Answer

Correct statements:

  1. Horizontal asymptote of y = 0: The horizontal asymptote remains the same as the original function, which is y = 0.

  2. Domain of {x| -∞ < x < ∞}: The domain of the function is all real numbers, as it is a transformation of an exponential function.

Incorrect statements:

  1. y-intercept at (0, 1): The y-intercept of g(x) is not at (0, 1) because the function is shifted horizontally.

  2. Horizontal asymptote of y = 2: The horizontal asymptote does not change to y = 2.

  3. y-intercept at (0, 4): The y-intercept is not at (0, 4) due to the horizontal shift.

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