Question

How can F(x)=6^x be transformed to g(x)=6^x - 5 - 7?

1.Multiply F(x) by 6.
2.Add 5 to F(x).
3.Subtract 7 from F(x).
4.Add 5 to the exponent of 6 in F(x).

Answer 1

To transform F(x)=6^x to g(x)=6^x - 5 - 7, we need to subtract 7 and then subtract 5 from F(x), resulting in g(x) = 6^x - 12. Other options mentioned alter the function in ways not consistent with the transformation required.

Step-by-step explanation:

The question was about transforming the function F(x)=6^x into the function g(x)=6^x - 5 - 7. To achieve this transformation, we apply the following steps:

1. Subtract 7 from F(x), transforming it to F(x) - 7.
2. Then subtract an additional 5 from the result, giving us the final transformed function g(x) = F(x) - 7 - 5, which simplifies to g(x) = 6^x - 12.

Note that the other options provided in the question are incorrect applications for this transformation:

• Multiplying F(x) by 6 changes the coefficient, not the constant term.
• Adding 5 to F(x) would increase the function's value, but we need to subtract.
• Adding 5 to the exponent would drastically change the graph, affecting the function's growth rate.

By performing these steps correctly, we transform F(x) into g(x) as required.