Question

Write a rule for g that represents a translation 2 units down, followed by a reflection in the y-axis of the graph of f(x)=5^x

Answer 1

Assuming that g(x) represents the transformed function, the rule for g can be obtained by applying the translation and reflection operations in the correct order.

To translate the graph of f(x) down by 2 units, we need to subtract 2 from the function. This gives us:

h(x) = f(x) - 2 = 5^x - 2

Next, we need to reflect the graph of h(x) in the y-axis. To do this, we replace x with -x in the function. This gives us:

g(x) = h(-x) = 5^(-x) - 2

Therefore, the rule for g(x) that represents a translation 2 units down, followed by a reflection in the y-axis of the graph of

f(x) = 5^x is:g(x) = 5^(-x) - 2