University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

149

Pages:

4
Author:

DSchneider

Transforming Graphs of Exponential and Logarithmic Functions A. VOCABULARY & CONCEPTS 1. Transformation Horizontal Translation Graph shifts left or right. Vertical Translation Graph shifts up or down. Reflection Graph flips over x- or y-axis. Horizontal Stretch or Shrink Graph stretches away from or shrinks toward y-axis. Vertical Stretch or Shrink Graph stretches away from or shrinks toward x-axis. Transformation f(x) Notation J(x - h) J(x) +k f(-x ) -J(x) f(ax) a • f(x) f(x) Notation Horizontal Translation Graph shifts left or right. j(x - h) Vertical Translation Graph shifts up or down. f(x) Reflection Graph flips over x- or y-axis. Horizontal Stretch or Shrink Graph stretches away from or shrinks toward y-axis. Vertical Stretch or Shrink Graph stretches away from or shrinks toward x-axis. +k f(-x) -J(x) Examples g(x) = 3 3 units right g(x) = 4x + 2 2 units left 4x - g(x) = 4x +5 g(x) = 4x - l g(x) = 4-x in the y-axis in the x-axis g(x) = 4 2x . Ju-ink by a factor of½ g(x) � -4r g(x) = 4.112 trctch by a factor of 2 g(x) = 3(4.r) stretch by a factor of 3 g(x) = ¼<4-f) shrink by a factor of¼ Example.s g(x) = 1og(x - 4) g(x) = log(x + 1) 3 units up I unit down g(x) = log(-.t) g(x) = -log x in the y-axis g(x) = log(½x) g(x) = 5 logx a• j(x) 4 units right 7 units left g(x) = log x + 3 g(x) = logx - I g(x) = log(4x) j(ax) 5 units up 1 unit down '1 g(x) = j logx in the x-axis shrink by a factor of¾ stretch by a factor of 3 -- stretch by a factor of 5 shrink by a factor off