10-6 Operations with Functions – We learned to combine functions using arithmetic operations, including addition, subtraction, and multiplication. Then we combined functions to solve real-world problems. We discovered that functions can be combined in the same way as numbers, expressions, and polynomials. Addition, subtraction, and multiplication can be used to find (f + g) (x), (f – g) (x), and (f x g) (x). Then Cameron completed the end-of-year Algebra 1 Test and did very well.
10-5 Compressions and Stretches of Functions – We learned to identify the effect on the graph of a function of multiplying the output by -1. Next we identified the effect on the graph of a function of replacing f(x) by k f(x) or f (k x) for specific values of k. We discovered that the graphs of functions are transformed when the input and output are multiplied by varying factors of k. Multiplying the output by a factor of k stretches or compresses the graph vertically. Multiplying the input by a factor of k stretches or compresses the graph horizontally.
Assignment: Complete the assigned problems for homework.
10-4 Translations of Functions – We graphed translations of absolute value, exponential, quadratic, and radical functions. Then we determined how combining translations affects the key features of the graph of a function. Then we learned that changes to the input and output of a function in the form f (x – h) + k result in a translation of the graph of the function. Adding a constant k to the output of the function shifts the graph vertically. Subtracting a constant h from the input of the function shifts the graph horizontally. Then we worked on an end-of-year Algebra 1 test on which Cameron is doing very well.
