Question

Respond to each of the following questions. Be sure to include and thoroughly describe each transformation.

Answer 1

Answer:

31. 1) Vertical shift up 4 units.

     2) Horizontal shift right 1 unit.

     3) Vertically stretched by a factor of 3.

32. $g(x)=-(x+3)^2+7$

Step-by-step explanation:

Some transformations for a function f(x) are shown below:

- If $f(x)+k$, the function is shifted up "k" units.

- If $f(x)-k$, the function is shifted down "k" units.

- If $f(x+k)$, the function is shifted left "k" units.

- If $f(x-k)$, the function is shifted right "k" units.

- If $-f(x)$, the function is reflected over the x-axis.

- If $bf(x)$ and $b>1$, the function is stretched vertically by a factor of "b".

31. Given the function $f(x)=x^{2}$ and the function $g(x) = 3(x - 1)^2 + 4$, we can notice that the transformations from the graph of f(x) to the graph of g(x) are:

1)  $f(x)+k$

2)  $f(x-k)$

3)  $bf(x)$, being $b>1$

Therefore, we can conclude that the transformations necessary to transform the graph of f(x) to the graph g(x) are:

1) Vertical shift up 4 units.

2) Horizontal shift right 1 unit.

3) Vertical stretch by a factor of 3.

32. Knowing the parent function:

 $f(x)=x^{2}$

And given the transformations:

1) Reflection over the x-axis.

2) Horizontal shift left 3 units.

3) Vertical shift up 7 units.

We can define that the function g(x) is:

$g(x)=-(x+3)^2+7$