The function ƒ(x) is modified as follows: It is multiplied by –3. x is replaced by x + 3. The new function is graphed. Which of the following effects on the graph of ƒ(x) are needed to produce the new graph? Choose all that apply.horizontal translationvertical translationdilationreflection over the x-axisreflection over the y-axis
Accepted Solution
A:
First the function f(x) is multiplied by -3. This involves 2 changes:
a) Multiplication by 3 This implies dilation
b) Multiplication by -1 This implies reflection of function over x-axis
Next x is replaced by x+ 3. This means the function is shifted to left by 3 units.
So this overall transformation results in following 3 changes: Horizontal Translation, Dilation and Reflection along x-axis