How do you graph #f(x)=3 sqrt (x-8)#?

Question

Avery Alexander · Accepted Answer

You can make a table of values for #f(x)# for various values of #x#
Remember that our functions is defined for #x>=8#

Hence its graph is

You can go to the link below where i have setup a desmos page to play with various values of f(x) which are then plotted so you get a feeling of the whole process.

desmos files for plotting f(x)

Isaiah Anthony · Answer

undefined To graph the function $ f(x) = 3\sqrt{x - 8} $, follow these steps:

1. Identify the parent function: The parent function for $ f(x) = \sqrt{x} $ is the square root function.
2. Determine the transformations: In the given function, there is a horizontal shift of 8 units to the right and a vertical stretch of 3 units.
3. Plot key points: Choose several values of $ x $ to find corresponding $ y $ values and plot these points on the graph.
4. Draw the graph: Connect the plotted points smoothly to form the graph of the function.

Remember to consider the domain of the function, which in this case, since it's a square root function, the value inside the square root ($ x - 8 $) must be greater than or equal to zero. This means $ x - 8 \geq 0 $, which implies $ x \geq 8 $. Thus, the domain of the function is $ x \geq 8 $.