Help with Graph Transformations

Question

 

(a) The graph of y=f(x+4) is the graph of y=f(x)

shifted horizontally ? and shifted vertically ?

(b) The graph of y=f(x)+1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically ?

(c) The graph of y=f(x−5)+1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically ?

(d) The graph of  y=f(x+5)−1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically

Answer 1

desmos.com/calculator/mo0uvkxcm0

Use the above Desmos graph to experiment with transformations of parent functions. The video only addresses horizontal and vertical shifts.

Answer 2

Hi Meghan W

(a) is 4 units left along the x axis

(b) is 1 unit up along the y axis

Please see below for rules that should help you do the rest.

There is a list of rules for Transformation of Linear Functions, that you can look up on the internet or in your text. First we can let the numerical value, the shift, be represented by the variables h and k: listed below are Rules for Transformation of a Linear Function Horizontally or Vertically.

For: y = f(x), y = f(x+h) shifts the line h units to the left horizontally along the x axis

For: y = f(x), y = f(x-h) shifts the line h units to the right horizontally along the x axis

For: y = f(x), y = f(x) + k shifts the line k units up vertically along the y axis

For: y = f(x), y = f(x) - k shifts the line k units down vertically along the y axis

I will answer (a) can you do the rest

The graph of y = f(x+4), where h = 4, is the graph of y = f(x) shifted 4 units to left horizontally along the x axis.

You can check and see the movement of your lines at desmos.com, on a graphing calculator and if you do the graphs by hand.

I hope this helps you to do the others.