Answer:
The function shown by the graph is [tex]f(x)=1+\frac{1}{2}\sqrt[3]{x-2}[/tex] ⇒ 1st answer
Step-by-step explanation:
To find the function chose two points from the graph and substitute their x-coordinates in each function, the right function we give you the corresponding y-coordinates
From the figure:
∵ The graph passes through points (2 , 1) and (3 , 1.5)
∵ [tex]f(x)=1+\frac{1}{2}\sqrt[3]{x-2}[/tex]
∵ x = 2
∴ [tex]f(2)=1+\frac{1}{2}\sqrt[3]{2-2}[/tex]
∴ [tex]f(2)=1+\frac{1}{2}\sqrt[3]{0}[/tex]
∴ [tex]f(2)=1+0[/tex]
∴ f(2) = 1 ⇒ same value of y-coordinate
∵ x = 3
∴ [tex]f(3)=1+\frac{1}{2}\sqrt[3]{3-2}[/tex]
∴ [tex]f(3)=1+\frac{1}{2}\sqrt[3]{1}[/tex]
∴ [tex]f(3)=1+\frac{1}{2}[/tex]
∴ f(3) = 1.5 ⇒ same value of y-coordinate
∴ The function shown by the graph is [tex]f(x)=1+\frac{1}{2}\sqrt[3]{x-2}[/tex]
