Functions Application Tasks

[dinosaur93]

1. Express the total surface area S of a cube as a function of the volume V of the cube?

2. Express the area of a equilateral triangle as a function of:
a. the length s of each side.
b. the altitude h.

3. A van travels half the distance of a journey at an average speed of 80km/h and half an average speed of x km/h. Define a function, S, which gives the average speed for the total journey as a function of x.

4. A cylinder is inscribed in a sphere with a radius of length 6 cm.



a. Define a function, V₁, which gives the volume of the cylinder as a function of the height (h) (State the rule and domain.)
b. Define a function, V₂, which gives the volume of the cylinder as a function of the radius (r) (State the rule and domain.)

5. The shape has area of A cm². Find A in terms of x. State the maximal domain and range which is defined if x + x + x < 9.

[pi]

This isn't a SAC right (kinda looks like one)? You really should have a go first yourself.

[monkeywantsabanana]

This isn't a SAC right (kinda looks like one)? You really should have a go first yourself.

Are you allowed to bring SACs home ?? :O

[pi]

This isn't a SAC right (kinda looks like one)? You really should have a go first yourself.

Are you allowed to bring SACs home ?? :O

Depends what school you are, we had one spesh SAC we could bring home.

[TrueTears]

yeah there are take home sacs XD

[b^3]

Really though SACS over the holidays? and ours were called assignments that you needed to be able to pass, but didn't contribute to your score

[dinosaur93]

haha, nah, these are just from some other book where I try and answer im my leisure time..

[pi]

haha, nah, these are just from some other book where I try and answer im my leisure time..

Haha, that's good then

Start with 1) then

1. Express the total surface area S of a cube as a function of the volume V of the cube?

Just some hints:



Try rearranging one of the above into and work from there

[dinosaur93]

err....kk

How do you do numbers 3, 4 and 5 then?

[brightsky]

3) average speed S = total distance travelled/time taken = d/(d/2*80 + d/2*x) = 160x/(x+80) [note that the 'd's cancel out].

4) draw the 2-d version of the diagram (that is, a square inscribed in a circle). mark in the centre of the circle. the radius is hence 'half' the diagonal of the square, so 2(r/2)^2 = 6^2, r^2 = 72, r = 6sqrt(2). also recognise that h = 2*r = 12 sqrt(2). should be able to complete the problem from here.

5) find the area of the shape by subtracting the x*x*x 'chunk' from the bigger 9*5x 'rectangle'.

[dinosaur93]

6. If f : [0, 2] R, where f(x) = sin 2x and g : [0, 2] R, where g(x) = 2 sinx then the value of (f + g) is _______?________

7. If f(x) = 3x², 0 x 6 and g(x) = , x 2 the domain of f + g is _____?_____

8. f is the function of defined by f(x) = , x R.  A suitable restriction for f, f* such that f*^-1 exists would be

a. f* : [-1, 1] R, f*(x) =

b. f* : R R, f*(x) =

c. f* : [-2, 2] R, f*(x) =

d. f* : [-1, ) R, f*(x) =

e. f* : [0, ) R, f*(x) =

9. Let h : [a, 2] R where h(x) = 2x - x². If a is the smallest real value such that h has an inverse function h^-1, then a equals
a. -1
b. 0
c. 1
d. -2
e.

10. If the angle between the lines 2y = 8x + 10 and 3x - 6y = 22 is , then is approximately by: Interesting Qs...
a. 1.17
b. 1.40
c. 2
d. 0.86
e. 1

[REBORN]

Q7.

Dom of f is [0,6]
Dom of g is (-inf,2]

Intersection gives [0,2]

[dinosaur93]

6. If f : [0, 2] R, where f(x) = sin 2x and g : [0, 2] R, where g(x) = 2 sinx then the value of (f + g) is _______?________

7. If f(x) = 3x², 0 x 6 and g(x) = , x 2 the domain of f + g is _____?_____

8. f is the function of defined by f(x) = , x R.  A suitable restriction for f, f* such that f*^-1 exists would be

a. f* : [-1, 1] R, f*(x) =

b. f* : R R, f*(x) =

c. f* : [-2, 2] R, f*(x) =

d. f* : [-1, ) R, f*(x) =

e. f* : [0, ) R, f*(x) =

9. Let h : [a, 2] R where h(x) = 2x - x². If a is the smallest real value such that h has an inverse function h^-1, then a equals
a. -1
b. 0
c. 1
d. -2
e.

10. If the angle between the lines 2y = 8x + 10 and 3x - 6y = 22 is , then is approximately by: Interesting Qs...
a. 1.17
b. 1.40
c. 2
d. 0.86
e. 1

anyone?

[samad]

f+g means f(x) + g(x). For q6, this means sin2x+2sinx then just sub in 3pi/2 for x for the answer

The domain of an addition (f+g) or product (f*g) function is the intersection of the domains of the two functions f and g. for q7 this means intersection of dom f and dom g, i.e dom (f+g) = [0,2]

For q 8, this is a reciprocal function that must be restricted so that it is one to one. Consider the function x² + 2, it is a parabola with one axial intercept at (0,2). The receprocal of this function has an axial intercept at (0, 1/2) and one asymptote, y=0. The turning point of the function is (0, 1/2). Therefore, to get a one to one function, we must have either (-infiinity, 0] or [0, infinity). Therefore, answer is E.