Answer:
Given function
[tex]f(x)=\dfrac{3}{4}\sqrt{x}[/tex]
Parent function
[tex]f(x)=\sqrt{x}[/tex]
The square root of a negative number cannot be taken, therefore the domain and range of the parent function are restricted:
- Domain: [0, ∞)
- Range: [0, ∞)
This means the parent function begins at the origin (0, 0) and is restricted to Quadrant I.
The only transformation the parent function has undergone is it has been multiplied by 3/4, which means it has been stretched vertically by a factor of 3/4. Therefore, the domain and range will not change.
The points shown on the given graphs are all where x = 4.
[tex]\textsf{Graphed function}: \quad f(4)=\dfrac{3}{4}\sqrt{4}=1.5 \implies (4,1.5)[/tex]
Therefore, the graph of the given function is the graph with:
- Domain: [0, ∞)
- Range: [0, ∞)
- Point: (4, 1.5)
