Noob prelim questions (1 Viewer)

[planino]

In which situations would squaring both sides be the best way to solve absolute values? Is it when they're in inequalities? Also, when would it be best to solve them 'normally' as opposed to solving by squaring?
How do we find horizontal asymptotes by using a table of values (not limits)?
Consider y = (x-2)² + 4, what changes on the Cartesian plane would be observed when we change the equation to y= 2(x-2)² + 4, and y=(x-2)²/2 + 4? I'm specifically referring to Ex 2J out of Cambridge y11 3U as I don't completely understand their explanation lol

 

[barbernator]

whenever you solve an absolute value question, you are effectively squaring both sides. eg |x|=2, x=+-2. Really we are just skipping a step, |x|=2, x^2=4, x=+-2. What do u mean by solving 'normally' anyway?

you should never find limits using a table of values, unless you are fairly confident in what the function is approaching and just making sure. Because if you just substitute an large number (1000) into a function that you don't know the shape of, there could still be a turning point or something else happening with the graph outside x=1000, so this is an inaccurate way of predicting the horizontal asymptote. Taking the limit is the best way to find the asymptotes. With basic graphs, finding horizontal asymptotes by inspection is also easy.

 

[RealiseNothing]

You don't need to square absolute values when working them out.

You take the two possible cases, by the definition of an absolute value:

or

You only square an expression when working with inequalities with a pronumeral in the denominator, or when dividing by a pronumeral. This is because when you multiply or divide by a pronumeral, you don't know whether or not the expression is positive or negative, so squaring it will ensure it is always positive. You need to know the sign of the expression as it can effect the inequality sign.

You solve them normally when there is an equals sign, as the sign of the expression doesn't have an effect.

 

[planino]

You don't need to square absolute values when working them out.

You take the two possible cases, by the definition of an absolute value:

or


You only square an expression when working with inequalities with a pronumeral in the denominator, or when dividing by a pronumeral. This is because when you multiply or divide by a pronumeral, you don't know whether or not the expression is positive or negative, so squaring it will ensure it is always positive. You need to know the sign of the expression as it can effect the inequality sign.

You solve them normally when there is an equals sign, as the sign of the expression doesn't have an effect.

When there are absolute values on both sides of the inequality, can we then solve by squaring since there'll be no effect on the sign?

 

[deswa1]

When there are absolute values on both sides of the inequality, can we then solve by squaring since there'll be no effect on the sign?

Yes because both sides are positive.

 

[planino]

whenever you solve an absolute value question, you are effectively squaring both sides. eg |x|=2, x=+-2. Really we are just skipping a step, |x|=2, x^2=4, x=+-2. What do u mean by solving 'normally' anyway?

you should never find limits using a table of values, unless you are fairly confident in what the function is approaching and just making sure. Because if you just substitute an large number (1000) into a function that you don't know the shape of, there could still be a turning point or something else happening with the graph outside x=1000, so this is an inaccurate way of predicting the horizontal asymptote. Taking the limit is the best way to find the asymptotes. With basic graphs, finding horizontal asymptotes by inspection is also easy.

for your last question, if you think about it in 2 steps, what we are doing to the parabola is, firstly dividing everything by 4, and then adding 3. So the parabola will widen by a factor of 4 and then be moved up the y axis 3 units.

Thanks! By solving 'normally', I meant e.g. |x| = 2, so x = +or- 2. Solving by that method (listing and solving both cases). When you're 'widening' by a factor of 4, do you draw the curve at x intercepts (if any) that are 4 times those of the original x-intercepts? Just another question though, why would you widen y = (x-2)2 + 4 by a factor of 4 and then be moved up the y axis 3 units when sketching y=(x-2)2/2 + 4?

 

[planino]

Yes because both sides are positive.

Got it, thanks

 

[JINOUGA]

When there are absolute values on both sides of the inequality, can we then solve by squaring since there'll be no effect on the sign?

Yes, in fact mathematically speaking, the positive square root is often used as part of the definition of what an absolute value is i.e. the absolute of x is the positive square root of x^2

 

[barbernator]

Thanks! By solving 'normally', I meant e.g. |x| = 2, so x = +or- 2. Solving by that method (listing and solving both cases). When you're 'widening' by a factor of 4, do you draw the curve at x intercepts (if any) that are 4 times those of the original x-intercepts? Just another question though, why would you widen y = (x-2)2 + 4 by a factor of 4 and then be moved up the y axis 3 units when sketching y=(x-2)2/2 + 4?

sorry i looked at the question wrong, i thought we were going from y= 2(x-2)2 + 4 to y=(x-2)2/2 + 4. disregard my answer

 

[planino]

sorry i looked at the question wrong, i thought we were going from y= 2(x-2)2 + 4 to y=(x-2)2/2 + 4. disregard my answer

Nws

Thanks guys!

 

[Carrotsticks]

Just a little note. Next time you ask a question, there is no need to say "Noob question" or anything of the sort.

A question is a question, best to not have this negative attitude =)