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) ________________________
x3
d) If y = is shifted 2 units to the right. d) _______________________
x2
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.
Answer: _______________
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
Give answer in interval notation.
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) ____________