which is the graph of the sequence defined by the function $f(x + 1)=\frac{3}{5}f(x)$ when the first term in…

Explanation:

Step1: Identify the type of sequence

The recurrence relation (f(x + 1)=\frac{3}{5}f(x)) with (f(1)=375) is a geometric - sequence. The general formula for a geometric sequence is (a_n=a_1r^{n - 1}), where (a_1) is the first - term and (r) is the common ratio. Here, (a_1 = 375) and (r=\frac{3}{5}).

Step2: Calculate the second term

When (x = 1), (f(2)=\frac{3}{5}f(1)). Substitute (f(1)=375) into the formula: (f(2)=\frac{3}{5}\times375 = 225).

Step3: Calculate the third term

When (x = 2), (f(3)=\frac{3}{5}f(2)). Substitute (f(2)=225) into the formula: (f(3)=\frac{3}{5}\times225 = 135).

Step4: Calculate the fourth term

When (x = 3), (f(4)=\frac{3}{5}f(3)). Substitute (f(3)=135) into the formula: (f(4)=\frac{3}{5}\times135 = 81).

The points of the sequence are ((1,375)), ((2,225)), ((3,135)), ((4,81)). The first graph is the correct one as it has these points plotted.

Answer:

The first graph.