Given:
(a)
(b)
Find-:
Check for linear, quadratic and exponential.
Explanation-:
Check for linear at the change in x and change of y is same.
(a)
Change of x and y
[tex]\begin{gathered} \Delta x=5-4 \\ \\ =1 \\ \\ \Delta y=48-96 \\ \\ =-48 \end{gathered}[/tex]Change of x and y is:
[tex]\begin{gathered} \Delta x=6-5 \\ \\ =1 \\ \\ \Delta y=24-48 \\ \\ =-24 \end{gathered}[/tex]So it is not a linear function
For exponential function: ratio is same for common difference
[tex]\begin{gathered} \text{ ratio}=\frac{96}{48} \\ \\ =2 \end{gathered}[/tex]For the second point
[tex]\begin{gathered} \text{ Ratio=}\frac{48}{24} \\ \\ =2 \end{gathered}[/tex]For the third point.
[tex]\begin{gathered} \text{ Ratio }=\frac{24}{12} \\ \\ =2 \end{gathered}[/tex]The ratio same so it is an exponential function.
(b)
The change in x and y is:
[tex]\begin{gathered} \Delta x=-2-(-1) \\ \\ =-1 \\ \\ \Delta y=-8-2 \\ \\ =10 \end{gathered}[/tex]Check
[tex]\begin{gathered} \Delta x=-1-(0) \\ \\ =-1 \\ \\ \Delta y=2-8 \\ \\ =-6 \end{gathered}[/tex]So it is not a linear function.
For exponential function.
[tex]\begin{gathered} \text{ Ratio=}\frac{-8}{2} \\ \\ =-4 \end{gathered}[/tex]Check for another point,
[tex]\begin{gathered} \text{ Ratio =}\frac{2}{8} \\ \\ =\frac{1}{4} \end{gathered}[/tex]So it is not a exponential function.
Check for quadratic function-:
If the double change of y is same so it is a quadratic function.,
So double difference is -4 for each point so it is a quadratic function.
