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? a) 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. b) both f(x) and g(x) include domain values of [�3, ?) and range values of (�?, ?), and both functions have an x-intercept in common. d) 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. d) 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

a) 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.

(not for the entire domain of f(x), only for the domain [3, infinity))

Explanation:

`f(x) = 3x\\g(x) = √(x - 3)`

The x- intercept of f(x) is at x = 0, y = 0.

The x- intercept of g(x) is at x = 3, y = 0.

So, they do not have the x-intercept in common,

g(x) does not have a y intercept i.e. it's domain is from 3 onward so it doesn't get to x = 0.

Hence they don't have a y- intercept in common.

Now, the domain of g(x) is [3, infinity)

and this interval is included in the domain for f(x)

and they both are positive for this interval not for the entire domain,

the entire domain for f(x) is from negative infinity to positive infinity.

But the only option that agrees with the above considerations (except for the domain part) is option a.