Consider the expression
To factorize the expression in the denominator we use difference of squares:
To factorize
we use the following method:
where a, b are 2 numbers such that a+b= -1, the coefficient of x,
and a*b= -6, the constant.
such 2 numbers can be easily checked to be -3 and 2
(-3*2=6, -3+2=-1)
So
for x>2
thus
for x>2,
Answer:
for x>2
, (but the expression is never 0)
Graphing, Substitution Method and Elimination Method
Mark because if you look at 0.(6) it is bigger than 0.(4)5
Okay I think there has been a transcription issue here because it appears to me there are two answers. However I can spot where some brackets might be missing, bear with me on that.
A direct variation, a phrase I haven't heard before, sounds a lot like a direct proportion, something I am familiar with. A direct proportion satisfies two criteria:
The gradient of the function is constant s the independent variable (x) varies
The graph passes through the origin. That is to say when x = 0, y = 0.
Looking at these graphs, two can immediately be ruled out. Clearly A and D pass through the origin, and the gradient is constant because they are linear functions, so they are direct variations.
This leaves B and C. The graph of 1/x does not have a constant gradient, so any stretch of this graph (to y = k/x for some constant k) will similarly not be direct variation. Indeed there is a special name for this function, inverse proportion/variation. It appears both B and C are inverse proportion, however if I interpret B as y = (2/5)x instead, it is actually linear.
This leaves C as the odd one out.
I hope this helps you :)
