Question

Match the functions to the ranges when the domain is (1,2) ...f(x)=3x + 5 F(x) = x^2 - 2x -5 F(x) =(x+5)x^2 F(x) =4-x

Answer 1

dommain is input
range is output from given input (domain)

1,2
just input 1 for x and evaluate
then input 2 for x and evaluate

f(x)=3x
f(1)=3(1)=3
f(2)=3(2)=6
range=(3,6)

f(x)=x^2-2x-5
f(1)=1^2-2(1)-5=1-2-5=-6
f(2)=2^2-2(2)-5=-5
range=(-6,-5)

f(x)=(x+5)x^2
f(1)=(1+5)(1^2)=(6)(1)=6
f(2)=(2+5)(2^2)=(7)(4)=28
range=(6,28)

f(x)=4-x
f(1)=4-1=3
f(2)=4-2=2
range=(3,2)

Answer 2

Answer:

Domain states that the set of all possible values of the independent variable for which function is defined.

Range states that the set of all resulting values of the dependent variables, when we substituted  the domain in a function.

Given: Domain (1, 2)

1. f(x) = 3x +5

for x = 1

f(1) = 3(1) +5 = 3 + 5 = 8

For x = 2

f(2) = 3(2) +5 = 6 + 5 = 11

Domain (1, 2) and Range (8, 11)

2. $f(x) =x^2-2x-5$

for x = 1

$f(1) =1^2-2(1)-5 = 1-2-5 = -6$

For x = 2

$f(2) =2^2-2(2)-5 = 4-4-5 = -5$

Domain (1, 2) and Range (-6, -5)

3. $f(x) =(x+5)\cdot x^2$

for x = 1

$f(1) =(1+5)\cdot 1^2 = 6 \cdot 1 =6$

For x = 2

$f(2) =(2+5)\cdot 2^2 = 7 \cdot 4 =28$

Domain (1, 2) and Range (6, 28).

4. f(x) =4 -x

for x = 1

f(1) = 4-1 = 3

For x = 2

f(2) = 4-x = 4-2 = 2

Domain (1, 2) and Range (3, 2)