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:

$f(x)=g(x)$ only at x= 0 and x= 1. They are not equal at x= 3.

Step-by-step explanation:

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

Substituting the values of x in the given function, we see that,

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

x= 0                 f(0)= 2×0+1= 1                     g(0)= 2×(0^2)+1= 1

x= 1                  f(1)= 2×1+1= 3                      g(1)= 2×(1^2)+1= 2+1 = 3

x= 3                 f(3)= 2×3+1= 7                    g(3)= 2×(3^2)+1= 18+1 = 19

Thus, from the graphs below and the above calculations, we have,

$f(x)=g(x)$ only at x= 0 and x= 1.