Identifying Functions

A relation is a rule that describes a relationship between two variables. It can be represented in various ways: verbally, as a set of ordered pairs, as an equation, or as a graph on a coordinate plane. A function is a particular kind of relation. This lecture series discusses how to recognize functions when they are given by different representations. Watch the videos and complete the interactive exercises.

Function rules from equations - Questions

Answers

1. y=5 x-26

To arrive at a correct equation, we have to solve the equation for y.

\begin{aligned} y+6 &=5(x-4) \\ y &=5(x-4)-6 \\ y &=5 x-20-6 \\ y &=5 x-26 \end{aligned}

The following equation is rearranged so x is the independent variable:

y=5 x-26


2. b=2-\frac{3}{4} a

To arrive at a correct equation, we have to solve the equation for b.

\begin{aligned} 3 a-7 &=-4 b+1 \\ 4 b-1 &=7-3 a \\ 4 b &=8-3 a \\ b &=\frac{8}{4}-\frac{3 a}{4} \\ b &=2-\frac{3}{4} a \end{aligned}

The following equation is rearranged so a is the independent variable:

b=2-\frac{3}{4} a


3. w=-\frac{7}{6} u

To arrive at a correct equation, we have to solve the equation for w.

\begin{aligned} 4 u+8 w &=-3 u+2 w \\ 6 w &=-7 u \\ w &=\frac{-7 u}{6} \\ w &=-\frac{7}{6} u \end{aligned}

The following equation is rearranged so u is the independent variable:

w=-\frac{7}{6} u


4. q=6 r+16

To arrive at a correct equation, we have to solve the equation for q.

\begin{aligned} q-10 &=6(r+1) \\ q &=6(r+1)+10 \\ q &=6 r+6+10 \\ q &=6 r+16 \end{aligned}

The following equation is rearranged so r is the independent variable:

q=6 r+16