Exercise 10 Page 528

Practice makes perfect

a Using the function f(x), we want to find the expression f(x)+2. To do this, we will add 2 to the given function and simplify.

f(x)=x^2-3

AddEqn

LHS+2=RHS+2

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

AddTerms

Add terms

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

We can describe this transformation as vertical translation 2 units up. It means that the graph of the given function was shifted 2 units up.

b Using the function f(x), we want to find the expression 2 * f(x). To do this, we will multiply the given function by 2 and simplify.

f(x)=x^2-3

MultEqn

LHS * 2=RHS* 2

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

Distr

Distribute 2

2 * f(x)=2x^2-6

We can describe this transformation as vertical stretch by a factor of 2.

c Using the function f(x), we want to evaluate for the given value, f( x+2). To do this, we need to substitute x+2 for x in each instance of the x-variable.

f(x)=x^2-3

Substitute

x= x+2

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

We can describe this transformation as horizontal translation 2 units left. It means that the graph of the given function was shifted 2 units left.

d Using the function f(x), we want to evaluate for the given value, f( 2x). To do this, we need to substitute 2x for x in each instance of the x-variable and simplify.

f(x)=x^2-3

Substitute

x= 2x

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

PowProd

(a * b)^m=a^m* b^m

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

CalcPow

Calculate power

f(2x)=4x^2-3

We can describe this transformation as horizontal stretch by a factor of 2.