Student Goals:

Students will be able to know the properties and identify the graphs of radical and piecewise functions.

The domain and range of the parents square root function are all nonnegative real numbers. The x-and y-intercepts of the parent square root function are both 0. It is increasing on its entire domain.

Do you remember when we looked at the absolute value functions that contains h inside the absolute value function and the k that is outside the function. The sign of the h that is inside the absolute value function is the opposite when you bring it out to graph. We are going to look at the square root functions the same exact way using h and k.

As you can see from the graph above, we see that inside the radical, there is an h which is a positive 1 and when you graph, it is always the opposite that is a negative 1 which is to the left 1 unit. However, the k stays the same so it is going downward 2 units.

The table and graph above shows the parent cube root function. The domain and range of the parent cube root function are all real numbers. The x-and y-intercepts of the parent cube root function are both 0. It is increasing on its entire domain.

The graph up above shows how we move the graph left 1 unit and up two units.

Lets go ahead and take a look at an example of a piecewise function.

A function you are already familiar with, the absolute value function, can be written as a piecewise function. you can give a piecewise definition of the absolute value function f(x)=|x| by writing f(x)={

Another example of a piecewise function is a step function. A step function is a function that pairs every number in an interval with a single value. The graph of a step function can look like the steps of a staircase. Each piece of the graph is a horizontal segment with any missing points indicated by open circles.