MATH 151 Lecture Notes - Lecture 5: Farad
Document Summary
Goal: given the graph y+f(x) we want to know how changing x or y affects the graph: basic idea: changing y (modifying values outside of the function) Changing x (modifying values inside the function) affects the graph horizontally. Vertical shifts: suppose k>0 is a fixed value (k is a positive constant) then the graph y= f(x)+k is a shift of y=f(x) k units on the graph. Reflections: the graph y=-f(x) is a reflection of y=f(x) across the x-axis. Vertical scaling: suppose a>0 is a fixed value then the graph y=a f(x) is a vertical scaling of y=f(x) Recall: modifying equations inside a function affects that function horizontally. Modifying it outside the function affects it vertically: note: when performing a sequence of transformation, they must be done in order. Slope intercept form of a line with a slope of m and a y-intercept (0,b) is y=mx+b. Special cases: horizontal lines have a slope of 0, vertical lines have undefined slopes.
