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. f(x)=2x+1
g(x)=2x^2+1

Answer 1

Answer:

$f(x)=g(x)$ at x= 0 and x= 1 and not at x= 3.

Step-by-step explanation:

We have the functions, $f(x)=2x+1$ and $g(x)=2x^2+1$.

It is given that,

At x=0, x=1, and x=3, $f(x)=g(x)$

i.e. $2x+1=2x^2+1$

i.e. $2x^2-2x=0$

i.e. $2x(x-1)=0$

i.e. x= 0 and (x-1)= 0

i.e. x= 0 and x= 1.

Also, after plotting the graphs of both the functions, we see their intersection point are (0,1) and (1,3).

Thus, we get that $f(x)=g(x)$ at x= 0 and x= 1 and not at x= 3.