Question

Write a formula for the function in the image below. 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!negative absolute value function with vertex at (2,3)The new equations f(x)=Answer

Answer 1

`f(x)=-\lvert x-2\rvert+3`

Explanation:

By the form of the graphed function we can state that it is involving an absolute value function, remember that absolute value at origin is given as:

Then, by the transformation rules of a function, we can determine what is the equation that represents the graph given:

*f(x)+d represents vertical translation up d units.

*f(x-c) represents horizontal translation to the right c units.

*-f(x) represents the reflection over the x-axis.

Now, we know that the absolute value function has a vertex at (2,3), which means a horizontal translation 2 units to the right, vertical translation 3 units up, and a reflection over the x-axis.

Hence, the new equation f(x) would be:

`f(x)=-\lvert x-2\rvert+3`