Block 3: Absolute value, irrational functions
Problem 1: Sketch a graph of a function:
a) y = |2x − 4|
b) y = |x + 1| − |1 − x|
c) y = x − |x − 2| − 4
Problem 2: Solve the equation:
a) 2|x − 1| − 6 = 0
b) |2x + 1| − |2x| + 1 = 2x
Problem 3: Solve in R:
a)
√
x − 3 −
√
2x + 5 = 0
b) 1 +
√
x + 1 = 2x
c)
√
x + 2 +
√
x − 1 =
√
3x + 3
d) x − 2 <
√
2x − 4
e) 1 − x >
√
5 − 2x
Block 4: Exponentials
Problem 1: Solve in R:
a) 2 · 31−x
= 18
b) 3x+2
+ 3x+1
+ 2 · 3x
= 126
c) 3x
+ 3x+1
− 5x−1
= 5x
− 3x+3
+ 5x+2
d) 4
25
x+3
· 125
8
4x−1
= 5
2
e) 4x
− 2x+1
− 8 = 0
f) 51−x
= 7x−1
g) 2x+1
+ 3 · 22+x
≤ 2x+5
Problem 2: Sketch a graph of a function:
a) y = 2x
b) y = 3−x
c) y = 1
3
x