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 \(-89\).