Factual Errors Report

"to equations in three dimensions" - we are only graphing two dimensional equations in Algebra 1.
Any system that uses a number line and one variable is one-dimensional (e.g. x = on a number line).
Any system that uses a cartesian coordinate system (x-y axis) is two-dimensional. "x" and "y" are the two dimensions respectively. ALL of Algebra 1 is done in one or two dimensions - it is outside the scope of the TEKS to add in 3 dimensional until Algebra 2.
Anything that is three dimensional as a graph would have an x, y, and z axis. There is NOT a z axis on the students models.

The physical graph in front of the students does have a third dimension - the height, but students will NOT be graphing with reference to the height. They will have fixed pegs representing one unit - a negligible height that is NOT considered a third dimension in these problems.

The given domain does not apply in this problem; the bird would start at 0 seconds, not -2 seconds. Thus, the domain should be 0 <= x <= 8.

This could offer additional discussion for "what does the y-intercept tell us about bird number 2?", "why does our domain end at 8?", and "is our domain discrete or continuous and why?"

1) A sequence is a "... ordered list of" NUMBERS, not "things."
2) Not all sequences are functions when paired with their term number. For instance, a_n = -1a_(n-1); let a_1 = 2 is a sequence whose outputs would be 2, -2, 2, -2... for the respective term numbers: 1, 2, 3, 4... This would not be a function if taken as ordered pairs.
There are two solutions to this error:
a) Change the word "function" in the last sentence to "relation."
b) Explain that some are not functions and some are. This would be more difficult and would take more effort; I would recommend the former.
3) "Term number" should be introduced in place of "place in the ordered list" to reinforce this vocabulary. "Term number" is an integral part of the definition of sequences.

"How do you determine if the rate of change is constant or a constant percent rate" - percent rate OF WHAT? This HAS to be defined. If it is a percent of an input value, then it is a constant rate of change - that is, it is linear. It is only exponential if it is a percent of the previous output value.

"an exponential function makes a smooth curve with a slope... that is constantly decreasing." This is incorrect. The first derivative of an exponential function is an exponential function - thus, the slope is not constantly decreasing - it is decreasing at the same rate as the output is decreasing. The slope of a function only decreases at a constant rate in quadratic functions - where the first derivative is linear, or constant.

"where r is the rate of change as a decimal." This is incorrect - r is not the rate of change - the rate of change would be a function f'(x) = (1 +/- r)^x*ln(1 +- r).
In this situation, r is not the rate of change, but the rate of GROWTH or DECAY - which is different.

That sentence is misleading, because it is not definitionally correct for a line of best fit. For a counter-example, consider a set of ten points that roughly follows the line y = x. If I have a line that intersects the line of best fit at a perpendicular angle, such that half of the points are on either side of the line, then I have fit the sentences parameters for the line, but it is most definitely NOT a line of best fit.
The line of best fit definitionally must follow the trend of the points - "following the _______ " being added to this sentence would fix this error.

"intercept" - should specify "y-intercept," and/or "x-intercept" - mathematically, we never discuss intercepts in the abstract, but have to specify. which specific intercept we are discussing (unless we are looking at the "intersection" of a system of equations, in which the word "intersection," not "intersect" would be correct).

This is not true - consider outliers. It would be better to say, "the majority of points should be close to the line" OR "all points, excluding outliers, should be close to the line."

This is false, it should designate - "the independent variable is in the exponent" OR "the input is in the exponent." Otherwise, the dependent variable or output could be in the exponent, which would make the function logarithmic, not exponential.

All three graphs have incorrect values graphed. The graph should reflect the problems.

Blue function's graph does not reflect the function correctly

"x2" should be written with an exponent of 2- x^2.