Linear vs Exponential
Look at the pattern of t(x) which are the y values.
Every time x goes up by 2 (from -3 to -1, or -1 to 1, 1 to 3, or 3 to 5), t(x) goes down by 2.5.
This means that there is a constant rate of change or slope and that the function is linear.
These points can be plotted on graph paper to see if they will make a line which they do :)

Here is some more practice from the awesome site www.emathinstruction.com

https://emathinstruction.com/wp-content/uploads/2014/11/CCAlg1-U6L8-Linear-Versus-Exponential.pdf

Residuals show how far the data is from the line of best fit.
If a line is a good fit for the data, then the residuals will be about half below and half above the x axis.  The residuals will also be close to the x-axis which means that their values are fairly small.
If the residual plot shows a pattern (see below), then a linear will not be a good fit.  See the link from Math Bits below:
http://mathbitsnotebook.com/Algebra1/StatisticsReg/ST2Residuals.html
Looking at the 4 choices, which looks most like the the left most graph that says “Random, No Pattern.  Linear Appropriate”?

Look at the graph above the minimum y value is -7 at the point (-3,-7).
We are looking for the y = that goes even  lower!!

Above is answer choice (1).  You can see the minimum y value is -2 (not less than -7)

Above is answer choice (2).  You can see the minimum y value is -6 (not less than -7)

Above is answer choice (3).  Whoa this one goes low!! Lower than the y value of the given graph way up above

Above is answer choice (4).  This graph does not go very low — it doesn’t even pass through the x-axis as its minimum y value is 2.