Question

for #1-4 determine the domain and range of each problem.
1.
a) domain: all real numbers
range: ( y geq -4 )
b) domain: ( y geq -4 )
range: all real numbers
c) domain: all real numbers
range: ( y > -4 )
d) domain: ( y > -4 )
range: all real numbers

2.
( y = 40(3)^x )
a) domain: all real numbers
range: ( y geq 0 )
b) domain: ( y geq 0 )
range: all real numbers
c) domain: all real numbers
range: ( y > 0 )
d) domain: ( y > 0 )
range: all real numbers

Explanation:

Step1: Analyze Problem 1 graph

The graph extends infinitely left/right (all real $x$), and touches $y=-4$, then rises.
Domain: $\text{All real numbers}$
Range: $y \geq -4$

Step2: Analyze Problem 2 function

$y=40(3)^x$ is exponential. $x$ can be any real number; $3^x>0$, so $y>0$.
Domain: $\text{All real numbers}$
Range: $y > 0$

Answer:

1. a) Domain: all real numbers, Range: $y \geq -4$
2. c) Domain: all real numbers, Range: $y > 0$