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.

Evaluate functions - Questions

Answers

1. g = -2

To find the output,g, we need to substitute 3 into the equation for r.

\begin{aligned} g &=-5 r+13 \\ g &=-5 \cdot 3+13 \\ &=-15+13 \\ &=-2 \end{aligned}

When the input is 3, the output is -2.


2. g = -43

To find the output, b, we need to substitute 6 into the equation for a.

\begin{aligned} b &=-1-7 a \\ b &=-1-7 \cdot 6 \\ &=-1-42 \\ &=-43 \end{aligned}

When the input is 6, the output is -43.


3. g = 22

To find the output, y, we need to substitute 5 into the equation for x.

\begin{aligned} y &=5 x-3 \\ y &=5 \cdot 5-3 \\ &=25-3 \\ &=22 \end{aligned}

When the input is 5, the output is 22.


4. g = -89

To find the output, k, we need to substitute -7 into the equation for t.

\begin{aligned} k &=10 t-19 \\ k &=10 \cdot-7-19 \\ &=-70-19 \\ &=-89 \end{aligned}

When the input is -7, the output is -89.