Parametrics...?

Can someone help me understand this?

This is from my Pre-Calculus Algebra class and this isn't in my book and of course, my professor hasn't gone over it.



.

Putting it into a calculator should be straightforward. Just set it to parametric mode.

Basically, instead of a function taking one argument (x) and transforming it into one value (y) as in y = 5x - 2, it's a function taking one argument (t) and transforming it into two values (x, y).

So for your problem, if t = 0, x = 0^3 = 0 and y = 0 - 2 = -2.

To convert to rectangular, you want to convert it to the form "y = (something)". You know that
y = t - 2
x = t^3

Treat it as a system of equations and solve for y in terms of x.

For part 3, insert the expression containing x in the inequality -3 <= t <= 5 and solve.

B, D, A

A parametric function is a graph that uses a parameter, t, to set the values for x and y. i.e. x and y are functions of the parameter, t, instead of y being a function of x, etc.

Therefore;
y - 2 = t;
x = t^3
x = (y - 2)^3
x^1/3 - 2 = y
B

t is restricted to -3 <= t <= 5;
therefore, since x = t^3
(-3)^3 <= x <= 5^3
-27 <= x <= 125
D

Graph result is A.
t = -3, y = -5, x = -27;
t = 0, y = -2, x = 0;
t = 5, y = 3, x = 125;

To graph it on a graphing calculator (Some sort of TI-Model should do), select MODE. It should say
Norma | Sci | Eng
Float | 01234...
Radian | Degree
Func | Par | Pol | Seq

You want Par selected, instead of Function.


A pineappleing ninja'd.

You both covered the other's missing point, so it's all good.

But the next one is weird.
Okay, x = t^2. -5 <= x <= 2
-5^2 = 25.
2^2 = 4
25 <= x <= 4 ...? Not possible, also not an answer choice.

You both covered the other's missing point, so it's all good.

But the next one is weird.
Okay, x = t^2. -5 <= x <= 2
-5^2 = 25.
2^2 = 4
25 <= x <= 4 ...? Not possible, also not an answer choice.

The bounds are on x, not t?