Answer:
The equation that matches the function shown is option;
C. [tex]y = sin\left (\dfrac{1}{2} \cdot x\right)[/tex]
Step-by-step explanation:
The given graph of the function is a sinusoidal graph
The values of 'x' and 'y' coordinates at the maximum, x-intercept and minimum points are given as follows;
x, [tex]{}[/tex] y
0 [tex]{}[/tex] 0
π [tex]{}[/tex] 1
2·π [tex]{}[/tex] 0
3·π [tex]{}[/tex] -1
4·π [tex]{}[/tex] 0
We note that sin(π/2) = 1, sin(π) = 0 sin(3·π/2) = -1, and sin(4·π/2) = sin(2·π) = 0
Therefore;
y = the sine of half the x-value
Which is presented as follows;
[tex]y = sin\left (\dfrac{1}{2} \cdot x\right)[/tex].
