ListaI

Prévia do material em texto

Lista de Func¸o˜es
Prof. Sidarta Lima
1. Questa˜o: Trace o gra´fico das seguintes func¸o˜es
f(x) = 2x + 5 g(x) = 4x− 3 h(z) = 4− z2 y = 4 + x2
f(y) = (x + 3)2 y = (x− 3)2 g(x) = x3 u(a) = −a3
x + 3y = 0 x− 3y = 0 2x− 5y = 0 2x + 5y = 0
y =
√
x− 3 y = −(x− 3)(1/2) y = |x| y = √2x
2. Questa˜o: Trace o gra´fico das seguintes func¸o˜es
f(x) =
{ −2 se x ≥ 3
2 se x < 3
h(x) =
{
2x− 1 se x ≥ 2
0 se 2 < x
u(x) =
{
x2 − 4 se x > −3
−2 se x ≤ 3
f(x) =
{
x2 − 4 se x < 3
2x− 1 se 3 ≤ x h(x) =
{
x− 2 se x < 0
x2 + 1 se x ≥ 0 u(x) =
{
6x + 7 se x ≤ −2
4− x se − 2 < x
f(x) =
 −5 se x < −11 se − 1 ≤ x ≤ 4
4 se x > 4
h(x) =
 x + 5 se x < −525− x2 se − 5 ≤ x ≤ 5
x− 5 se x > 5
3. Questa˜o: Dada a func¸a˜o f(x) = 2x− 1 calcule
(a) f(3) (b) f(−2) (c) f(0) (d) f(a + 1) (e) f(x + 1)
(f) f(2x) (g) 2f(x) (h) f(x + h) (i) f(x) + f(h) (j)
f(x + h)− f(x)
h
4. Questa˜o: Dada a func¸a˜o f(x) = 2x2 + 5x− 3 calcule
(a) f(−2) (b) f(−1) (c) f(0) (d) f(3) (e) f(h + 1)
(f) f(2x2) (g) f(x2 − 3) (h) f(x + h) (i) f(x) + f(3) (j) f(x + h)− f(x)
h
5. Questa˜o: Dada a func¸a˜o g(x) = 3x2 − 4 calcule
(a) g(−4) (b) g(1/2) (c) g(x2) (d) g(3x2 − 4) (e) g(x− h)
(f) g(x)− g(h) (g) f(x + h)− f(x)
h
6. Questa˜o: Dada a func¸a˜o f(x) = 3/x calcule
(a) f(1) (b) f(−3) (c) f(6) (d) f(1/3) (e) f(3/a)
(f) f(3/x) (g) f(x− 3) (h) f(x)− f(3) (i) f(3)
f(x)
(j)
f(x + h)− f(x)
h
7. Questa˜o: Dada a func¸a˜o h(x) =
2
x + 1
calcule
(a) h(3) (b) h(−3) (c) h(x− 1) (d) g(x)− g(1) (e) g(x2)
(f)
g(x + h)− g(x)
h