The true statement about h(x) is: The function is increasing on the interval [0, ∞).
Linear Function
A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:
a= the slope.If:
a> 0 , the function is increasing;
a< 0 , the function is decreasing;
b=the constant term that represents the y-intercept.
Domain and Range
The domain of a function is the set of input values for which the function is real and defined. In other words, when you define the domain, you are indicating for which values x the function is real and defined.
While the domain is related to the values of x, the range is related to the possible values of y that the function can have.
You should convert the text of the question into a math expression.
[tex]h(x)=3*\sqrt{x}[/tex]
Like the coefficient a is greater than zero (a>0), the function is increasing.
The equation has a square root, so, the values of x can not present negative values. Therefore, x≥0. Consequently, the values of y (range) for this function will be greater than or equal to zero (y≥0). See the attached image.
The range is:
[tex]{Solution:}\:&\:f\left(x\right)\ge \:0\:\\Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]
Learn more about the range and the domain here:
brainly.com/question/10197594
