Question

Im confused on how to do these questions. Transformation of functions.

Answer 1

Given a parent function below

`f(x)=|x|`

Find the absolute value vertex. In this case, the vertex for

`y=|x|`

To find the x coordinate of the vertex, set the inside of the absolute value x equal to 0. In this case x = 0

Replace the variable x with 0 in the expression

y = |0|

The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0

y = 0

The absolute value vertex is (0,0)

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

`(-\infty,\infty)`

For each x value, there is one y value. Select few x values from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.

`\begin{gathered} y=|x|,\text{ i.e} \\ x=-3,y=3 \\ x=-2,y=2 \end{gathered}`

(b) The domain of a graph consists of all the input values shown on the x-axis which are -3, -2, -1, 0, 1, 2, 3

(c) The range is the set of possible output values, which are shown on the y-axis which are 3, 2, 1, 0, 1, 2, 3