In the last task, we (hopefully) discovered that adding a constant to the range of a function translates the function vertically. [br]1. Make a conjecture: What will happen if we add a constant to the domain (input) of a function?[br]2. Below, fill in the columns for the range of the functions with the given domain. Use the following rules for your functions:[br][math]f\left(x\right)=\left|x\right|[/math][br][math]g\left(x\right)=f\left(x-3\right)[/math][br][math]h\left(x\right)=f\left(x+2\right)[/math][br][br]When you've found all of the range values for [i]f,[/i] [i]g, and h[/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
1. Think about the [b]inputs[/b] you used when finding your points. When x was 1, what did you [i]actually[/i] plug into the functions?[br]2. What appears to be the effect of subtracting 3 from the input of a function?[br]3. 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][br][math]f\left(x\right)=\left|x\right|[/math][br][math]a\left(x\right)=f\left(2x\right)[/math][br][math]b\left(x\right)=f\left(\frac{1}{2}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. Think about the [b]inputs[/b] you used when finding your points. When x was 1, what did you [i]actually[/i] plug into the functions?[br]2. What appears to be the effect of multiplying the input of a function by 2?[br]3. Generalize: How does the graph of f(x) compare to the graph of f(kx)?