SOLUTION: Draw a rough sketch of the following function. Use your basic shapes and shifting. f(x)= (square root of) x-4

Algebra ->  Inequalities -> SOLUTION: Draw a rough sketch of the following function. Use your basic shapes and shifting. f(x)= (square root of) x-4      Log On


   

Question 107446: Draw a rough sketch of the following function. Use your basic shapes and shifting.
f(x)= (square root of) x-4
Found 2 solutions by Edwin McCravy, MathLover1:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

       ___
f(x)= Öx-4

The 4 shifting rules are:

1. If +C is added to the right side of f(x), the graph is shifted
   +C units UPWARD
2. If -C is added to the right side of f(x), the graph is shifted
   +C units DOWNWARD
3. If x+C is substituted for x in the right side of f(x), the graph
   is shifted C units TO THE LEFT
4. If x-C is substituted for x in the right side of f(x), the graph
   is shifted C units TO THE RIGHT

We observe that the right side of the equation 
        ___
f(x) = Öx-4

is just like the right side of the equation 
     _
y = Öx

which has as its graph the green curve below:

 

except that x-4 is substituted for x in the right side of f(x),
so rule 4 applies and the graph is shifted 4 units TO THE RIGHT
like the green curve on the right below:



Then we erase the green curve on the left that was shifted, and
the final graph is:

 

Edwin

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+sqrt%28x+-+4%29
We can find for what x is +sqrt%28x+-+4%29+=+0, and we will see that for f, it'll be x+%3E=4, because any x%3C4 will give us the square root of a negative number which is undefined.
f%28x%29 is defined for all real x excluding 4,
or from (-+infinity to4] and from[4 to infinity)
to solve this,
sqrt%28x+-+4%29+=+0 raise both sides of an equation to a second power
%28sqrt%28x+-+4%29%29%5E2+=+0%5E2
x+-+4+=+0
x++=++4
to sketch it, you will need at least two points because the graph will be a line (it is linear function):
x+ | +f%28x%29
0+ | +-4
4+ | +0

here is the graph:
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=1%2Ax-4 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-5

y=1%2A%28-5%29-4

y=-5-4 Multiply

y=-9 Add

So here's one point (-5,-9)




Now lets find another point

Plug in x=-4

y=1%2A%28-4%29-4

y=-4-4 Multiply

y=-8 Add

So here's another point (-4,-8). Add this to our graph





Now draw a line through these points

So this is the graph of y=1%2Ax-4 through the points (-5,-9) and (-4,-8)


So from the graph we can see that the slope is 1%2F1 (which tells us that in order to go from point to point we have to start at one point and go up 1 units and to the right 1 units to get to the next point) the y-intercept is (0,-4)and the x-intercept is (4,0)


We could graph this equation another way. Since b=-4 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-4).


So we have one point (0,-4)





Now since the slope is 1%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-4), we can go up 1 units



and to the right 1 units to get to our next point


Now draw a line through those points to graph y=1%2Ax-4


So this is the graph of y=1%2Ax-4 through the points (0,-4) and (1,-3)