Today, we're going to explore how to change the graph of a function by adding to the function's equation.[br]Below, fill in the columns for the range of the two functions with the given domain. Use the following rules for your functions:[br][math]f\left(x\right)=\left|x\right|[/math] [math]g\left(x\right)=f\left(x\right)-3[/math][br][br]When you've found all of the range values for [i]f[/i] and [i]g[/i], graph the points on the coordinate plane by selecting both columns ([i]x[/i] and [i]f(x)[/i]) and creating a list of points[icon]/images/ggb/toolbar/mode_createlistofpoints.png[/icon]
1. Look at the individual points you graphed above. How do the outputs from g differ from the outputs from f?[br]2. What appears to be the effect of subtracting 3 from a function?[br]3. Make a conjecture: what would happen if you graphed a new function [math]h\left(x\right)=f\left(x\right)+2[/math]?[br]Test your conjecture by graphing h(x) above (type |x|+2 in an empty cell)[br]4. Generalize: How does the graph of f(x) compare to the graph of f(x)+k? (use your vocabulary from geometry!)
Below, fill in the columns for the range of the two functions with the given domain. Use the following rules for your functions:[br][math]f\left(x\right)=\left|x\right|[/math] [math]a\left(x\right)=2f\left(x\right)[/math] [math]b\left(x\right)=\frac{1}{2}f\left(x\right)[/math][br][br]When you've found all of the range values for [i]f,[/i] [i]a, and b[/i], graph the points on the coordinate plane by selecting both columns ([i]x[/i] and [i]f(x), for example[/i]) and creating a list of points
1. Look at the individual points you graphed above. How do the outputs from a and b differ from the outputs from f?[br]2. What appears to be the effect of multiplying the outputs of a function?[br]3. Generalize: How does the graph of f(x) compare to the graph of k·f(x)? (might need some new vocabulary for this one)