How do I find the stretches of a transformed function?

Question

Do I look for the x and y intercepts and the invariant points?

Lincoln Anderson · Accepted Answer

Look at the variables of #a# and #b# to figure out what factor to stretch by.

Refer to: #y=af(b(x-h))+k# A vertical stretch is the stretching of a function on the x-axis. If #|a|>1#, then the graph is stretched vertically by a factor of #a# units. If the values of #a# are negative, this will result in the graph reflecting vertically across the x-axis. A horizontal stretch is the stretching of a function on the y-axis. If #|b|<1#, then the graph is stretched horizontally by a factor of #b# units. If the values of #b# are negative, this will result in the graph reflecting horizontally across the y-axis. For example: #y=2f((1/2)x-h))+k# #a=2# #b=1/2# To vertically stretch we use this formula: #y^1=ay# #y^1=2y# So, the vertical stretch would be by a factor of 2. To horizontally stretch we use this formula: #x^1=x/b# #x^1=x/(1/2)# #x^1=2x# So, the horizontal stretch would be by a factor of 2 as well. Extras: If #|a|<1#, this results in a vertical compression. If #|b|>1#, this results in a horizontal compression.

Cora Alexander · Answer

undefined To find the stretches of a transformed function, you need to examine the coefficients of the function's equation.

1. For a vertical stretch (or compression) of a function, look at the coefficient of the function's variable inside the function itself. If the coefficient is greater than 1, the function is vertically stretched. If it's between 0 and 1, it's vertically compressed.

2. For a horizontal stretch (or compression), look at the coefficient of the variable inside the function's argument (such as x). If the coefficient is greater than 1, the function is horizontally compressed. If it's between 0 and 1, it's horizontally stretched.

3. If there's a negative sign in front of the function, it reflects the function across the x-axis. If there's a negative sign within the function (e.g., f(-x)), it reflects the function across the y-axis.

Remember, these transformations affect the graph of the function but not its essential shape or characteristics.