The resulting function g(x) is ...
g(x) = f(x +1)
g(x) = (((x +1) +1)(x +1) -2)(x +1) +1
= ((x +2)(x +1) -2)(x +1) +1
= (x² +3x)(x +1) +1
= x³ +4x² +3x +1

The shifted function g(x) is ...
g(x) = x³ +4x² +3x +1

7 0

3 years ago

The population of Laredo, Texas, was about 215,000 in 2007. It was about 123,000 in 1990,

Gnom [1K]

$\text{Hello there!}\\\\\text{We're trying to find the rate of change of the population}\\\\\text{We see that the population increased over time, meaning that our rate of}\\\text{change would be positive}\\\text{We know that:}\\\\\text{In 2007 = 215,000 people}\\\\\text{In 1990 = 123,000 people}\\\\\text{Subtract 215,000 by 123,000}\\\\215000-123000= 92,000\,\text{increase in the population}\\\\2007-1990 = 17\,\text{years}\\\\\text{Divide 92,000 by 17}\\\\92000\div17=5,411.76\\$

$\text{Round to the nearest whole number:}\\\\5,412\\\\\boxed{\text{Rate of change: 5,412}}$

6 0

3 years ago