Answer:
31. 1) Vertical shift up 4 units.
2) Horizontal shift right 1 unit.
3) Vertically stretched by a factor of 3.
32. [tex]g(x)=-(x+3)^2+7[/tex]
Step-by-step explanation:
Some transformations for a function f(x) are shown below:
- If [tex]f(x)+k[/tex], the function is shifted up "k" units.
- If [tex]f(x)-k[/tex], the function is shifted down "k" units.
- If [tex]f(x+k)[/tex], the function is shifted left "k" units.
- If [tex]f(x-k)[/tex], the function is shifted right "k" units.
- If [tex]-f(x)[/tex], the function is reflected over the x-axis.
- If [tex]bf(x)[/tex] and [tex]b>1[/tex], the function is stretched vertically by a factor of "b".
31. Given the function [tex]f(x)=x^{2}[/tex] and the function [tex]g(x) = 3(x - 1)^2 + 4[/tex], we can notice that the transformations from the graph of f(x) to the graph of g(x) are:
1) [tex]f(x)+k[/tex]
2) [tex]f(x-k)[/tex]
3) [tex]bf(x)[/tex], being [tex]b>1[/tex]
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:
[tex]f(x)=x^{2}[/tex]
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:
[tex]g(x)=-(x+3)^2+7[/tex]
