Exercise 40 Page 279

Looking at the graphs of the given exponential functions, we see that the graph of f(x)= 13(6)^x is translated h units to the left.

Notice that the point (- 1,2) is on the graph of g(x)= 13(6)^(x-h). Let's substitute it in and solve for h.

g(x)= 13(6)^(x-h)

SubstituteII

x= - 1, y= 2

2= 13(6)^(- 1-h)

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Solve for h

MultEqn

LHS * 3=RHS* 3

6=6^(- 1-h)

a=a^1

6^1=6^(- 1-h)

EquateExponents

Equate exponents

1=- 1-h

AddEqn

LHS+1=RHS+1

2=- h

DivEqn

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

- 2= h

RearrangeEqn

Rearrange equation

h=- 2

The value of h is - 2.