Question

Taylor graphs the system below on her graphing calculator and decides that f(x)=g(x) at x=0, x=1, and x=3. Provide Taylor some feedback that explains which part of her answer is incorrect and why it is incorrect.

Answer 1

The part of her answer is incorrect is that f(x)=g(x) at x=3, because this value is not in the solution of the equation f(x)=g(x)

Explanation:

f(x)=g(x)

2x+1=2x²+1

This is a quadratic equation. Equaling to zero: Subtracting 2x and 1 from both sides of the equation:

2x+1-2x-1=2x²+1-2x-1

0=2x²-2x

2x²-2x=0

Common factor 2x:

2x(x-1)=0

Two solutions:

x=0

and

x-1=0

Solving for x: Adding 1 both sides of the equation:

x-1+1=0+1→x=1

Then f(x)=g(x) at x=0, and x=3