Question

module: 25sm-mt-t16 m2
1
in the (xy)-plane, the graph of the equation (y = 3^x) is translated 6 units down. what is an equation of the resulting graph ?
a (y = -6(3)^x)
b (y = 3^{(x + 6)})
c (y = 3^x - 6)
d (y = 3^{(x - 6)})

Explanation:

Step1: Recall vertical translation rule

For a function \( y = f(x) \), translating it \( k \) units down gives \( y = f(x)-k \).

Step2: Apply the rule to \( y = 3^x \)

Here, \( f(x)=3^x \) and \( k = 6 \) (translated 6 units down). So the new equation is \( y = 3^x-6 \).

Answer:

C. \( y = 3^x - 6 \)