# 3

Document Sample

```					                           Self-Assessment C
Functions and relations
Name: ______________________
1. Find the linear function (give the equation in the form y=mx+b)
4
a) With slope            and y-intercept=-2                              a) _______
7
b) Through the points (-1,3) and (4,-5)                                  b) _______

3
2. If f(x) =       x  1,    g(x)=2x3+1 and h(x)=x2+3, find
2
a) h(3)                                                                                   a) ________

b) g(-2)                                                                                  b) ________

c) f(-15)                                                                                 c) ________

d) g(m)                                                                                   d) ________

e) h(x2)                                                                                  e) ________

f)   g 1  15)                                                                         f) ________

g)   g  f (4)                                                                          g) ________

h) (fg)(4)                                                                                h) _________

3
x            f(x)                     x        g(x)                  Find
1            -2                       0        3                     a) g(3)
3            4                        -2       5                     b) g(-2)
5            3                        4        1                     c) f(5)
7            0                        3        7                     d) g(3)
e) f(1)
1
f) f (4)

g)    f 1 ( g 1 1)
i) (fg)(3)
j) ( g  f )(7)

 x if x  2

4. Consider the functions f(x)=|x| and       g(x) =  x| if  3  x  2
|
x 2 if x  3

a) f( 3)                                                                a)_________

b) f(-9)                                                                b) _________
c) g(-2)                                                             c) _________

d) g(-3)                                                             d) _________

e)g (5)                                                              e) _________

5. Consider the graph of the mathematical relation given below:
y=f(x)
5
4

2
1

-7          -3               3        6            9                   x

-4

a) Is this relation a function?                                                a) __________

b) Is this relation a one-to-one function?                                     b) __________

c) Give domain in interval notation:                                           c) __________

d) Give the range in interval notation.                                        d) __________

e) Find f(0)                                                                   e) __________

f) Find f(3)                                                                   f) __________

g) Find f(-7)                                                                  g) __________

h) Find all values of x for which f(x)=0                                       h)__________

i) Find all values of x for which f(x)= -4                                     i) __________

j) Find f(5)+f(6)                                                              j) _________

k) Find f(f(-3)+6)                                                             k) _________

L) Find f(9) +6                                                                L)_________

m) Find the y-intercept                                                        m) _________

n) Find the x-intercepts.                                                      n)__________

p) Find the values of the domain for which the function is increasing          p) __________

q) Find the values of the domain for which the function is decreasing          q) __________
6. Indicate which of the following functions are even, odd or neither
a) f(x)= x(x2+5)                                                                      a)_____________

b) f(x)=3x + x2                                                                       b)_____________

c) f(x)= (x2+1)2                                                                      c)_____________

d) f(x)= x(x5-6)                                                                      d)_____________

e) f(x)=3 + 4x + x3                                                                   e)_____________

f) f(x)= x(x2+1)3                                                                     f)_____________

7. Test for symmetry with respect to the y-axis, the x-axis or the origin.
a) y=-2                                                                               a)_____________

b) x=-5                                                                               b)_____________

c) 5xy - 7 = x2                                                                       c)_____________

e) x3 + 4x = y                                                                        e) ____________

f) 2xy + 3 = x2                                                                       f)_____________

g) 5x + y2 = 7                                                                        g)____________

8. Find the equation that results if the graph of

a) x2+ y2= 9 is shifted 2 units to the right and 4 units downward. a) _______________________

b) y = 3x-5 is shifted 3 units to the left.                            b) _______________________

c) y-3 = 2(x+1)2 is shifted 1 unit to the right and 3 units up.         c) ________________________

x3
d) If y =           is shifted 2 units to the right.                    d) _______________________
x2

e) If   y  3x 2  2 x  3     is shifted 2 units to the left and 3 units downward.

e) __________________
y
 2 if x  3

9. Graph f ( x )   x if  2  x  3                                                   x
2 x  1 if x  2


10. If f(x) = x2+ 2 and g(x) =3x - 4, find

a) (fg)(x)=__________________                  b) (fog)(x)=________________________

c) (gof)(x)=____________________                 d) (fogof)(0)=____________________

e) f(m)=____________________

11. If f(x) =2x+3, and g(x)=x3 -3, find
a) g-1(x)                                                          a) ________

b) (f+g)(2)                                                        b) ________

c) (fg)(1)                                                         c) ________

d) (gof)(-3)                                                       d) ________

e) g-1(5)                                                           e) _______

f) f-1(-5)                                                         f) _______

12. Find f-1(x) for each of the following functions:
a) f(x)=2x3-8                                                           a)________________

x 3
b) f(x)=                                                                b)________________
2x  5

`

13. m varies directly as p and inversely as r+3. If m=1 when p=5 and r=2, find m when p=4 and r=-2.

14. Find the vertex and line of symmetry of the parabola y= -2x2 +12x -17
Give the domain and range. Graph.
Vertex: _______
y                                     line of symmetry:_______
domain: ________
range: ________

x

15. Sketch the graph of the following functions or relations:

a) y = |x-3| + |x+2|                               b) y≤ x- |x-2|
y                                                               y

x                                                      x

c) (x2 - 3x - 4)(y2 - 4) = 0                      d) (x - 3)2+ y2 < 9

y                                                          y

x                                                     x

16. Find the vertex and line of symmetry of the parabola y-3 = -2(x +2)2.
Give the domain and range. Graph.
Vertex: _______
y                                       line of symmetry:_______
domain: ________
range: ________

x
17. Find the vertex and line of symmetry of the parabola y= 2x 2 -12x +17
Give the domain and range. Graph.
Vertex: _______
y                                      line of symmetry:_______
domain: ________
range: ________

x

18. Find the vertex and line of symmetry of the parabola y= -2x2 -5x +3
Give the domain and range. Graph.
Vertex: _______
y                                            line of symmetry:_______
domain: ________
range: ________

x

19. Use the result of problem 18 to find the solution of the inequality   -2x2 -5x +3 ≥ 0
18. _____________

20. Find the solution of the inequalities. Give answer in interval notation

a)      3x  5  x  2

a) ________

x   1
b)      
6 x 1
b) ____________

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 46 posted: 12/13/2011 language: English pages: 6