Answer to Question #240869 in Calculus for CCW

Question

Unit 1 Review:

5) What is domain of

f(x) = { 3x + 2, -3 < x < 1

-2x + 5, 1 < x < 4

6) What is range of

f(x) = { 3x+2, -3 < x < 1

-2x + 5, 1 < x < 4

Answer 1

Given that: $f(x) = \begin{cases} 3x+2 &\text{if } -3<x<1 \\ -2x+5 &\text{if } 1<x<4 \end{cases}$

(1) From the given data, we can say directly that the domain of the function is: $x\in(-3,1)\cup(1,4)$

(2) Range:

At $x=-3,f(-3)=-9+2=-7\\$

At $x=1, f(1)=3+2=5$

At $x=4, f(4)=-8+5=-3$

So, range of $f(x)$ is: $(-7,5)$