Question

Write a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=x^2 is shifted up 1 unit and to the left 2 units.The new equations f(x)=Answer

Answer 1

Given the function f(x) defined as:

`f(x)=x^2`

We need to obtain the graph after performing two shifts: 1 unit up and 2 units left. For the first shift, we do the transformation:

`f(x)\rightarrow f(x)+1`

Now, for the second shift:

`f(x)\rightarrow f(x+2)`

Combining these transformations:

`\begin{gathered} f(x)\rightarrow f(x+2)+1 \\ \therefore f(x)=(x+2)^2+1 \end{gathered}`