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Here are a few recommended readings before getting started with this lesson.
There are different ways to represent a function — using tables of values, mapping diagrams, graphs, and equations. However, aside from these, one of the most common ways is using function notation.
y equals f of x.Equations that are functions can be written using function notation.
Besides f, other letters such as g or h can be used to name the function. Similarly, letters other than x can name the independent variable.
In the same way that an expression can be evaluated at a particular x-value, functions can also be evaluated at a specific input. Furthermore, it is also possible to determine the input that produces a specific output.
For the last few days of the long holiday, Izabella and Emily visited a city they did not know. Before returning home, they went into a souvenir shop where all the souvenirs were priced the same. After picking out some gifts and just before paying, Emily found a $3 gift card in her purse.
The function C(s)=4.5s−3 represents the cost, in dollars, of buying s souvenirs with a $3 gift card.
C(s)=69
LHS+3=RHS+3
LHS/4.5=RHS/4.5
Calculate quotient
Rearrange equation
x=1
Add and subtract terms
Multiply
Subtract term
V(x)=21
Distribute 9and-3
Add and subtract terms
LHS/12=RHS/12
Calculate quotient
Rearrange equation
x=g(x)
f(g(x))=h(x)
g(x)=x−5
Distribute 2
Add terms
Izabella and Emily are shopping for pants. Both girls have a $3 discount coupon for the store. After choosing a pair of pants each, they discovered that the pants are 25% off the marked price. The girls could not agree which order of discount would save them more money, so the cashier allowed them to apply the discounts in whichever order they wanted.
The function f(x)=x−3 represents the effect of applying only the coupon to the marked price, while g(x)=43x represents the effect of applying only the store's sale discount to the marked price. In both functions, x represents the marked price.
x=f(x)
g(f(x))=I(x)
f(x)=x−3
x=31
Subtract term
ca⋅b=ca⋅b
Calculate quotient
x=g(x)
f(g(x))=E(x)
g(x)=43x
E(x)=21
LHS+3=RHS+3
LHS⋅4=RHS⋅4
LHS/3=RHS/3
Rearrange equation
Marked Price | Amount Paid | |
---|---|---|
Izabella's Pants | $31 | $21 |
Emily's Pants | $32 | $21 |