Question 3 (15 points)

Question

1)Describe the transformations that must be applied to the graph of each power function, f(x), to obtain the transformed function.
Then, write the corresponding equation. i State the domain and range of the
transformed function. For even functions, state the vertex and the equation of the axis ot symmetry.
4
5(2)-2,2-5⅔(2-3) +1

Answer 1

To obtain the transformed function, we need to apply the following transformations:

1) Vertical shift down 2 units: f(x) ➔ f(x) - 2
2) Horizontal compression by a factor of 1/5: f(x) ➔ f(5x)
3) Vertical stretch by a factor of 3: f(x) ➔ 3f(x)
4) Vertical shift up 1 unit: f(x) ➔ f(x) + 1

The corresponding equation for the transformed function is:

5(2)-2,2-5⅔(2-3) +1 ➔ 3[5(2)-2,2-5⅔(2-3) +1 ] - 2

Domain: All real numbers
Range: All real numbers

For even functions, there is a vertex at the axis of symmetry. The vertex for this transformed function is at (0,1) and the equation of the axis of symmetry is x = 0.