Section 1.1: A Review of Functions

What is a function?

A function is a rule that assigns to each value in the domain, D, exactly one value in the

range, R.

Ex 1) Let f(x) = 2x – 3. Find

a) f(–5)

b) f(2)

Ex 2) Use the vertical line test to identify graphs in which y is a function of x.

a) b) c) d)

Ex 3) Determine whether the relations are functions:

b) c)𝑎) 2𝑥 + 𝑦2 = 16 𝑦 = 𝑥2 + 1 𝑦 = 𝑐𝑜𝑠𝑥

Once we know we have a rule that is a function, we want to know what the domain and range are for the


Ex 4) Let and𝑓 𝑥( ) = 𝑥+1𝑥−2 𝑔 𝑥( ) = 𝑥 + 2

Find the domain of each function.

Ex 5) Let f(x) = 2x – 3. State the domain of the function, and find:

a) f(–5)

b) f(2)

c) f(a +1)

d) f(x + h)

Ex 6) Simplify the difference quotient for𝑓 𝑥+ℎ( )−𝑓(𝑥)

ℎ 𝑓 𝑥( ) = 3 − 𝑥2

Piecewise Functions:

Ex 7) Graph the piecewise function 𝑓 𝑥( ){𝑥2 − 2𝑥 + 1 𝑓𝑜𝑟 𝑥 < 2 𝑥 − 1| | 𝑓𝑜𝑟 𝑥 ≥2

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