Answer:
See explanantion
Explanation:
Solution:-
- We will start of with the given function y = x^3, and plot a small sketch.
First transformation:-
- We multiply the y = x^3, with a constant a = 1/3. Where,
y1 = a*y
Where, a : real constant
- The cases for a:
a > 1 ----> makes the function steeper
0 < a < 1 ----> Flattens the graph/less steep
a < - 1 ------ > Reflection about x-axis and makes the function steeper.
0 < a < -1 ----> Flattens the graph/less steep and reflection about x-axis
- For a = 1/3, the graph flattens or in other words with increasing value of "x" the value of "y" increases at a decreased rate.
Second Transformation:-
- We add the b = 5 to the resulting graph y = 1/3*x^3.
y2 = 1/3*x^3 + b
Where, b : Real constant
- The cases for b:
b > 0 --------> Vertical upward shift of the graph by b units
b < 0 ---------> Vertical downward shift of the graph by b units
- For b = 5 > 0, The graph 5 units up or in other words the y-intercept shifts from y = 0 to y = 5.
- The required function y = 1/3*x^3 + 5 undergoes two transformation. a = 1/3 flatten out the starting function y = x^3 and b = 5 shifts the resulting graph vertically upwards.