Formative assessment

Question

Graph the function  f(x) =2 - sqrt x +6.  State the range of this function.

Answer 1

Hi Cameron,

The range is all values f(x) or "y" can be.

 

f(x) = 2 - √(x+6)

 

You can not take the square root of a negative number so (x+6) ≥ 0 making √(x+6) ≥ 0

 

Then the function becomes;

f(x) = 2 - 0

or

f(x) = 2 - (+number)

 

as the positive number increases, f(x) goes to negative infinity due to the negative sign in front of it.

 

Use this graphing calculator:

https://www.desmos.com/calculator

Range is "all y ≤ 2"

 

 

Answer 2

The range is the all real numbers between 2 and 0 and 0 and -ve infinity, as the domain is between -6, and +ve infinity, an x value smaller than minus 6 results in a sqrt of a -ve number , the smalles value x can take is -6, with a corresponding y value of 2, and the largest value x can take is any real number that is larger than -6 including 0 The range is all the y values corresponding to X values , Range = [2,0] & [0,-inf] or y<=2 if you Plug in x values larger than -6 you get corresponding values of y. If you plot the resulting points on a Cartesian system of coordinates, you will get a curve.