Exercise 22 Page 532

Practice makes perfect

a Using the function f(x), we want to find the expression f(x)-1. To do this, we will subtract 1 from the given function.

f(x)=(x-3)^2

SubEqn

LHS-1=RHS-1

f(x)- 1=(x-3)^2- 1

We can describe this transformation as vertical translation 1 unit down. It means that the graph of the given function was shifted 1 unit down.

b Using the function f(x), we want to find the expression - 1 * f(x). To do this, we will multiply the given function by - 1 and simplify.

f(x)=(x-3)^2

MultEqn

LHS * (- 1)=RHS* (- 1)

- 1 * f(x)= - 1 * (x-3)^2

MultNegPos

(- a)b = - ab

- 1 * f(x)=- (x-3)^2

We can describe this transformation as a reflection in the x-axis.

c Using the function f(x), we want to evaluate for the given value, f( x-1). To do this, we need to substitute x-1 for x in each instance of the x-variable and simplify.

f(x)=(x-3)^2

Substitute

x= x-1

f( x-1)=( x-1-3)^2

SubTerm

Subtract term

f(x-1)=(x-4)^2

We can describe this transformation as horizontal translation 1 unit right. It means that the graph of the given function was shifted 1 unit right.

d Using the function f(x), we want to evaluate for the given value, f( - 1x). To do this, we need to substitute - 1x for x in each instance of the x-variable and simplify.

f(x)=(x-3)^2

Substitute

x= - 1x

f( - 1x)=( - 1x-3)^2

IdPropMult

Identity Property of Multiplication

f(- 1x)=(- x-3)^2

NegBaseToPosBase

(- a)^2=a^2

f(- 1x)=(x+3)^2

We can describe this transformation as a reflection in the y-axis.