Question

When the graph of a certain function f(x) is shifted 2 units to the right and stretched vertically by a factor of 2 relative to the x-axis (meaning that all y-coordinates are doubled), the resulting graph is identical to the original graph.

Given that f(0)=1, what is f(10)?

Answer 1

Given the properties of the function f(x), which remains identical after specific transformations, we conclude that f(10) is equal to f(0), and since f(0) = 1, we find that f(10) = 1 as well.

Step-by-step explanation:

The question asks us to determine the value of f(10) given that the function f(x) is such that when its graph is shifted 2 units to the right and vertically stretched by a factor of 2, it remains identical to the original graph. Also, we know that f(0) = 1. Since the vertically stretched and shifted graph is identical to the original, it suggests that f(x) is a periodic function with a period of 2 units (the horizontal shift) and it is even (since the vertical stretch does not affect its symmetry).

Considering these properties, the value of the function at x = 10, which is 5 periods of 2 units to the right of x = 0, would be the same as the value at x = 0. Hence, f(10) would be equal to f(0), and therefore, f(10) = 1.

Answer 2

Ma yasakō lāgi māphī cāhanchu.