Math Help - A little help sir

1. A little help sir

Q. If the domain of the fxn y=5+3x is the set {x: 1 ≤ x ≤ 4} find the range of the fxn and express it as a set..

2. Originally Posted by ranthrave
Q. If the domain of the fxn y=5+3x is the set {x: 1 ≤ x ≤ 4} find the range of the fxn and express it as a set..
$1 \leq x \leq 4 \Rightarrow 3 \leq 3x \leq 12 \Rightarrow 8 \leq 5+3x \leq 17$

So the range is the set $\{y: 8 \leq y \leq 17\}$

3. Originally Posted by ranthrave
Q. If the domain of the fxn y=5+3x is the set {x: 1 ≤ x ≤ 4} find the range of the fxn and express it as a set..
Alternatively notice that $f(x)$ is increasing $\forall{x}\in\mathbb{R}$

Therefore we should have that $x_0

So the maximum on this interval should be $f(\text{smallest x-value})$ and the largest $f(\text{largest x-value})$

So

$f(1)\leq{y}\leq{f(4)}\Rightarrow{8\leq{y}\leq{17}}$