Answer:
Because of the range of the sine function.
Step-by-step explanation:
The reason why the value of the sine ratio for an acute angle
of a right triangle must always be a positive value less
than 1 has to do with the the range of the sine function.
The range of the sine function is
But in the first quadrant all y-values are positive and acute angles are less than 90°.
Therefore the range will now be 0≤y<1 for acute angles.
Given:
The parent function is
Consider the transformed function is g(x) instead of f(x) because both functions are different.
Step-by-step explanation:
We have,
It can be written as
...(i)
The translation is defined as
.... (ii)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.
If k is negative, then f(x) is reflected across the x-axis to get g(x).
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (i) and (ii), we get
, f(x) shifts 4 units right.
, f(x) shifts 8 units down.
, it is negative so f(x) reflected across the x-axis.
, so f(x) stretched vertically by factor 5.
Therefore, the function f(x) reflected across the x-axis, stretched vertically by factor 5 and shifted 4 units right 8 units down to get g(x).