Exercise 39 Page 279

Looking at the graphs of the given exponential functions, we see that the graph of f(x)=- 3^x is translated h units to the right.

Notice that the point (4,- 1) is on the graph of g(x)=- 3^(x-h). Let's substitute it in and solve for h.

g(x)=- 3^(x-h)

SubstituteII

x= 4, y= - 1

- 1=- 3^(4-h)

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Solve for h

DivEqn

.LHS /(- 1).=.RHS /(- 1).

1=3^(4-h)

DiffInExponent

a^(m-n)= a^m/a^n

1=3^4/3^h

MultEqn

LHS * 3^h=RHS* 3^h

3^h=3^4

EquateExponents

Equate exponents

h=4

The value of h is 4.