Graph the relation and check whether it is a function.
If it is not a function draw a vertical line.
{(2, 3), (3, 0), (2, 2)}
{(–3, 2), (3, 0), (–2, 3), (2, –3)}
{(4, 3), (4, –3), (–3, –2), (3, 2)}
Find the domain of the relation, draw its graph and tell whether the relation is a function.
{(x, y): |x| = |y| and | x| 2}
{(x, y): |y| = xand x 4}
{(x, y): |x| + |y| = 3}
{(x, y): |x + y| = 0 and | y| 1}
{(x, y): |y| = 3 and | x| 2}
{(x, y): |xy| = 3}
{(x, y): |x|y = 3}
Find the range of the function.
F: x 4 – 3x
Domain = {0, 1, 2, 3}
g: x x2 – 3
Domain = {–2, 0, 2}
f: x x2 – 4x
Domain = {–1, 0, 1, 2, 3}
G: x x2 – 5x + 5
g: x x4 – x2
Domain = {–3, 0, 3}
m: z 3 – |x|
Domain = {–2, –1, 0, 2}
Graph the function.
g: x x3 – x2
m: z 3 – |x|D = {–2, –1, 0, 2}
Find the value of f(g(1)) and g(f(1)) if f(x) = x2 – 2and g(x) = 2 – 3x.
Find the value of f(g(2)) and g(f(2)) if f(x) = x2 – 2 and g(x) = 2 – 3x.
Find the value of f(f(2)) and f(2f(1)) if f(x) = x2 – 2.
Find the value of:
if f(x) = x2 – 2 and g(x) = 2 – 3x.
Find the value of g(a +1) – g(a) if g(x) = 2 – 3x.
if f(x) = x2 – 2.
Prove f(0) = 0 if f(x + y) = f(x) + f(y), for all real numbers x and y.
Prove f(2x) = 2f(x) if f(x + y) = f(x) + f(y), for all real numbers x and y.
Prove f(–x) = –f(x) if f(x + y) = f(x) + f(y), for all real numbers x and y.
{(x,y): |x| = |y| and | x| 2}
{(x,y): |y| = x and x 4}
{(x,y): |x| + |y| = 3}
{(x,y): |x + y| = 0 and | y| 1}
{(x,y): |y| = 3 and | x| 2}
{(x,y): |xy| = 3}
{(x,y): |x|y = 3}
g: x x4 –x2
g: x x3 –x2
