Question

1. kiki tracked her yearly income from 2010 to 2016 in the scatterplot.

between which years did her income decrease?
scatterplot image
a between 2010 – 2011 only c between 2010 – 2011 and 2012 – 2013
b between 2012 – 2013 only d between 2010 – 2011 and 2013 – 2014

1. in the graph shown, on which interval is the graph decreasing?

graph image
a ( x leq -3 )
b ( -3 leq x leq -1 )
c ( x geq -1 )
d ( x geq 3 )

Explanation:

Question 16

Step1: Analyze the scatter - plot trend

A decreasing trend means the income value (y - value) is lower at the later year (x - value).
For the period \(2010 - 2011\): The income at \(2010\) is higher than the income at \(2011\).
For the period \(2012 - 2013\): The income at \(2012\) is higher than the income at \(2013\).
For the period \(2013 - 2014\): The income at \(2013\) is lower than the income at \(2014\).

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is decreasing on an interval \((a,b)\) if for any \(x_1,x_2\in(a,b)\) with \(x_1Looking at the graph:

• For \(x\leq - 3\): As \(x\) increases (moving from left - to - right), \(y\) increases.
• For \(-3\leq x\leq - 1\): As \(x\) increases (moving from left - to - right), \(y\) decreases.
• For \(x\geq - 1\): As \(x\) increases (moving from left - to - right), \(y\) increases.

Answer:

C. between \(2010 - 2011\) and \(2012 - 2013\)

Question 17