Answer:
y=5 cos πx
Explanation:
In the graph of the cosine function:
One full cycle goes from x = 0 to x = 2, this means that the period of the graph is 2.
For the general cosine function:
[tex]f(x)=a\cos(bx+c)+d[/tex]
The period is determined using the formula:
[tex]Period=\frac{2\pi}{b}[/tex]
Thus, to have a period of 2, the value of b must be π.
The options that satisfy these properties are:
[tex]\begin{gathered} y=5\cos\pi x \\ y=-5\cos\pi x \end{gathered}[/tex]
Next, the low point on that cycle is (1, — 5).
[tex]\begin{gathered} \text{ When }x=1:y=5\cos\pi x=5\cos\pi(1)=-5 \\ \text{When }x=1:y=-5\cos\pi x=-5\cos\pi(1)=5 \end{gathered}[/tex]
The function of these two that contain (1, -5) is y=5 cos πx.
The function that could have this graph is y=5 cos πx.
