Question

Let y = |x+m|+ s;

where m ≠0 and s ≠0.
Explain how the values of m and
S affect the graph of the function
as compared to the graph of
Y = |x|

Answer 1

The values of m and s in the function y = |x + m| + s affect the graph by shifting it horizontally (m) and vertically (s). Positive m shifts the graph right and negative m left, while positive s shifts it up and negative s down.

Step-by-step explanation:

The function y = |x + m| + s where m ≠ 0 and s ≠ 0 can be seen as a transformation of the basic absolute value function y = |x|. The value m shifts the graph horizontally, and the value s shifts it vertically. If m>0, the graph moves right; if m<0, it moves left. A positive s value moves the graph up, while a negative s value moves it down.

Let's analyze the effect of these parameters. When m is positive, we expect the 'V' shape of the absolute value function to be translated to the right by m units. Similarly, if m is negative, the graph shifts to the left by |m| units. The parameter s represents the vertical shift. If s is positive, the entire graph is lifted upwards by s units, and if it is negative, it is lowered by |s| units.