Question

What key features do the functions f(x) = 3x and g of x equals the square root of the x minus 3 end root have in common?

1-Both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.
2- Both f(x) and g(x) include domain values of [–3, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
3- Both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions have a y-intercept in common.
4- Both f(x) and g(x) include domain values of [–3, ∞) and range values of (–∞, ∞), and both functions increase over the interval (–3, 0).

Answer 1

Functions can be represented using equations and graphs

The key features are (1) both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.

How to determine the key features

The functions are given as:

$f(x) = 3^x$

$g(x) = \sqrt{ x - 3}$

Using a graphing calculator:

• The domain of g(x) is $[3,\infty)$
• The range of g(x) is $[0,\infty)$
• The domain of f(x) is $(-\infty,\infty)$
• The range of f(x) is $(0,\infty)$
• Both functions have positive values for their domains

By comparing the above highlights, the true statement between functions g(x) and f(x) is option (1)

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