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Big Ideas Math Integrated I, 2016 View details

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Exercise 2 Page 326

Identify the equation of the graph.

f(- 7)=128

Practice makes perfect

We are asked to find f(- 7). Let's analyze the graph of f.

First, we will identify the equation of the graph. We know that the function f is an exponential function. y=a* b^xNotice that the points ( 0, 1) and ( - 2, 4) belong to the graph. We will find values of a and b by substituting the coordinates of these points into the equation.

y=a* b^x

SubstituteII

x= 0, y= 1

1=a* b^0

ExponentZero

a^0=1

1=a* 1

MultByOne

a * 1=a

1=a

Let's substitute 1 for a into the equation. y= a* b^x ⇓ y= 1* b^x ⇓ y=b^x Next, we will substitute ( - 2, 4) for x and y to find b.

y=b^x

SubstituteII

x= - 2, y= 4

4=b^(- 2)

▼

Solve for b

RaiseEqn

LHS^(- 12)=RHS^(- 12)

4^(- 12)=(b^(- 2))^(- 12)

PowPow

(a^m)^n=a^(m* n)

4^(- 12)=b^1

ExponentOne

a^1=a

4^(- 12)=b

NegExponentToFrac

a^(- m)=1/a^m

1/4^(12)=b

RootToPowD

sqrt(a)=a^(1n)

1/sqrt(4)=b

CalcRoot

Calculate root

1/2=b

RearrangeEqn

Rearrange equation

b=1/2

Let's substitute 12 for b into the equation. y= b^x ⇓ y=( 1/2)^x Therefore, the function is f(x)=( 12)^x. Finally, we will find f( - 7) by substituting - 7 for x.

f(x)=(1/2)^x

Substitute

x= - 7

f( - 7)=(1/2)^(- 7)

▼

Simplify right-hand side

PowQuot

(a/b)^m=a^m/b^m

f(- 7)=1^(- 7)/2^(- 7)

BaseOne

1^a=1

f(- 7)=1/2^(- 7)