3.1

pg 145 # 1-12

2025-03-17

1.

a) linear, first difference is consistent
b) quadratic, 2nd difference are all 1
c) linear, first diff is 4
d) quadratic, 2nd diff is 2

2

a) up
b) down
c) down
d) up

3

a) 2, -6
b) down
c) $x=-2$

4

a) $(-2,3)$
b) $x=-3$
c) $$
\begin{align}
& R={y\in \mathbb{R};y\leq {3} } \
& D={x \in \mathbb{R}}
\end{align}

# 5 a) ```functionplot --- --- f(x) = x^2 -3 ``` b) ```functionplot --- --- f(x) = -3(x+3)^2 +4 ``` c) ```functionplot --- --- f(x) = 2(x-4)(x+2) ``` d) ```functionplot --- --- f(x) = -1/2x^2 +4 ``` # 6 a) $y_{int}=3$

\begin{align}
& f (x) = -3(x-1)^2+6 \
& f(x) = -3(x-1)(x-1)+6 \
& f (x) = -3x^2+6x+3
\end{align}

$$b)$$

\begin{align}
& f(x) = 4(x-3)(x+7) \
& f(x) = 4(x^2-3x+7x-21) \
& f(x) = 4x^2 -12x+28x-84 \
& f(x) = 4x^2 + 16x-84
\end{align}

$y_{int} = -84$ j # 6 a) b) c) d) # 6 a) b) c) d) # 6 a) b) c) d)