24. f(x) = sin² x, g(x) = 1 − cos 2x 25. f(x) = ex sin x, g(x) = e* cos x

7. Four students write equations. Do Now-5/7/21 Student 1 y=-5 Student 2 y=- -+21 14-x Student 3 y = Student 4 -8+7 y = Which student writes the equation of a linear function? A Student 1 B Student 2 C Student 3 D Student 4

Consider the relation between hours of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P¡ = (0, 5) (ii) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) (iii) Student 3 spent two hours studying and received 8 in the quiz. P3 : (2, 8). %3| We want to find a linear relation between hours of study and grade of the quiz y = mx + q where m and q are our unknowns, x represents the hours studied for the quiz and y the quiz grade. (4а Show that there is no line y = mx + q that passes through P , P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P, P, P3 in the line equation and show that the 3x2 system with unknowns m and g has no solutions. (4b Write the system of equations for part a) in matrix form Aš b where i = (m, q)" . (4c Compute (AT A)-1. (4d Compute i (AT A)-' A™ b and find m = x1 and q = x2. (4e Plot the line obtained by replacing m and q and the…

2. Determine the definition of the piece wise linear function shown in each of the graphs  3. Consider the following sets of data points. Decide in which cases you would chose a piecewise linear model to fit the data points.  4. For any part of question 3 that was suitable for meddling with piecewise linear function: a) draw this model “by eye” b) estimate the value of y when x=12  6. Consider the set of data points in the table