Question

What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common? Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common. Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common. Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.

Answer 1

The statement about both functions that is true is:

• Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

What is the domain and range for the function of y = f(x)?

The domain of a function is the set of values of input for which the function is valid.

The range is the dependent variable of a set of values for which the function is defined.

Given that:

f(x) = 4 - x

• The slope (m) of the function = -1
• x-intercept = (4,0)
• y-intercept = (0,4)
• Domain =  [4,∞)

For function g(x) = -1 ×$\mathbf{\sqrt{x-4}}$

• The domain = x ≥ 4 and the solution set is [4,∞)
• The range g(x) = ≤ 0 and the solution set is [-∞, 0)
• The function g(x) does not have a y-intercept.

Therefore, from the given options, the statement about both functions that is true is:

• Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

Learn more about the domain of a function here:

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