Questions: Let f(x)=3x If g(x) is the graph of f(x) shifted right 1 units, write a formula for g(x) g(x)=

Solution Steps

To find the formula for \( g(x) \) when the graph of \( f(x) = 3|x| \) is shifted right by 1 unit, we need to adjust the input \( x \) in the function \( f(x) \). Shifting a function to the right by 1 unit involves replacing \( x \) with \( x - 1 \) in the function's formula.

1. Start with the given function \( f(x) = 3|x| \).
2. To shift the function to the right by 1 unit, replace \( x \) with \( x - 1 \).
3. The new function \( g(x) \) will be \( 3|x - 1| \).

The original function is given by: \[ f(x) = 3|x| \]

To shift the function \( f(x) \) to the right by 1 unit, we replace \( x \) with \( x - 1 \): \[ g(x) = 3|x - 1| \]

Using the given \( x \) value of 2: \[ f(2) = 3|2| = 3 \cdot 2 = 6 \] \[ g(2) = 3|2 - 1| = 3 \cdot 1 = 3 \]

Final Answer