Question

Transformations can be described as follows: a times f(b(x-h))+k. Highlight what to expect for each of these transformations a, b, h, and k.

Answer 1

In function transformations, the parameters a, b, h, and k control the vertical stretch/compression and reflection, horizontal stretch/compression and reflection, horizontal shift, and vertical shift, respectively. They shape how the graph of a function is manipulated.

Step-by-step explanation:

Transformations of functions can be described by the expression a times f(b(x-h))+k, where each of the parameters a, b, h, and k have specific effects:

• a: This parameter affects the vertical stretching or compression of the graph. If a is greater than 1, the graph stretches; if 0 < a < 1, it compresses. A negative a value reflects the graph over the horizontal axis.
• b: This parameter affects the horizontal stretching or compression of the graph. A value of b greater than 1 compresses the graph horizontally, while 0 < b < 1 stretches it. A negative b reflects the graph over the vertical axis.
• h: This value represents the horizontal shift. If h is positive, the graph shifts to the right; if it's negative, to the left.
• k: This value affects the vertical shift. A positive k moves the graph upwards, while a negative k shifts it downwards.

Knowing these parameters helps in understanding how a function's graph is transformed. For example, a phase shift could be represented by the parameter h in trigonometric functions.