First slide

Functions (XII)

Question

$T h e n u m b e r o f l i n e a r f u n c t i o n s w h i c h m a p s$ $[- 1, 1]$ $o n t o$ $[0, 2] i s$

Moderate

A

0
B

1
C

2
D

>2

Solution

$Let f (x) = c x + b$
(1) $\Rightarrow f (- 1) = 0, f (1) = 2 \Rightarrow a = b = 1 \Rightarrow f (x) = x + 1$
$(2) \Rightarrow f (- 1) = 2, f (1) = 0 \Rightarrow a = - 1, b = 1 \Rightarrow f (x) = - x + 1$

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