Question

First, find the increasing functions. Then, classify each increasing function as having a larger or a smaller unit rate than the function represented in the graph.

Answer 1

To identify the increasing functions you need to identify the unit rate (rate of change) in each function, to be an increasing function the unit rate needs to be a possitive amount.

In a equation written in the form y=mx+b the unit rate is m

Then, for the given functions the increasing functions are:

`\begin{gathered} y=(4)/(3)x-(5)/(3) \\ \\ y=(5)/(4)x-3 \\ \\ y=(7)/(4)x-(9)/(4) \\ \\ y=(6)/(5)x-(3)/(5) \\ \\ y=(8)/(5)x-(7)/(5) \end{gathered}`

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To idenify the unit rate of the graphed function use two points (x,y) in the next formula:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ \text{Points: (0,-2)(2,1)} \\ \\ m=(1-(-2))/(2-0)=(1+2)/(2)=(3)/(2) \end{gathered}`

Then, for the given increasing functions the next have a larger unit rate:

`\begin{gathered} m=(3)/(2)=1.5 \\ \\ \\ y=(7)/(4)x-(9)/(4)(m=(7)/(4)=1.75) \\ \\ y=(8)/(5)x-(7)/(5)(m=(8)/(5)=1.6) \end{gathered}`

And for the given increasing function the next have a smaller unit rate:

`\begin{gathered} m=(3)/(2)=1.5 \\ \\ y=(4)/(3)x-(5)/(3)(m=(4)/(3)=1.33) \\ \\ y=(5)/(4)x-3(m=(5)/(4)=1.25) \\ \\ y=(6)/(5)x-(3)/(5)(m=(6)/(5)=1.2) \end{gathered}`