Translating the function f(x) = 5x two units to the right yields g(x) = 5(x - 2). Distributing, g(x) simplifies to 5x - 10. Therefore, the translated function is g(x) = 5x - 10.
When a function is translated two units to the right, it means that each value of x is replaced by x - 2 in the original function. In this case, the original function is f(x) = 5x. To find the expression for the translated function, substitute (x - 2) for x in the original function:
f(x) = 5x
Translated function: g(x) = 5(x - 2)
Now, distribute the 5 into the parentheses:
g(x) = 5x - 10
Therefore, the expression for the function obtained by translating f(x) = 5x two units to the right is g(x) = 5x - 10. This means that for any given x-value, the corresponding y-value of the translated function is 10 units less than the y-value of the original function. Graphically, this translation shifts the entire graph of the original function horizontally to the right by two units.
Understanding translations in functions is crucial in mathematics as it allows us to manipulate and analyze functions in various ways, providing insights into their behavior and relationships.
Complete question below:
"If a function is represented by f(x) = 5x, what is the expression for the function obtained by translating it two units to the right?"