Question

The graph of ( g(x) ) is the result of translating the graph of ( f(x) = 1/2 ) three units to the left. What is the equation of ( g(x) )?

a) ( g(x) = 1/2 left(x + 3right) )
b) ( g(x) = 1/2 left(x - 3right) )
c) ( g(x) = 1/2x - 3 )
d) ( g(x) = 1/2x + 3 )

Answer 1

The equation of g(x) is g(x) = 1/2(x + 3).

Step-by-step explanation:

The equation of g(x) is (g(x) = 1/2(x + 3).

To translate the graph of f(x) = 1/2 three units to the left, we need to subtract 3 from the input value of f(x). This can be represented as f(x - 3). So the equation of g(x) becomes g(x) = f(x - 3) = 1/2(x - 3).

We can simplify this equation to g(x) = 1/2(x + 3) by distributing the negative sign.