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+1g(x)=2x2+1

at x= 0 and x= 1 and not at x= 3.

Step-by-step explanation:

We have the functions, and .

It is given that,

At x=0, x=1, and x=3,

i.e.

i.e.

i.e.

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 at x= 0 and x= 1 and not at x= 3.

only at x= 0 and x= 1. They are not equal at x= 3.

Step-by-step explanation:

We have the functions, and

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

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,

only at x= 0 and x= 1.

Step-by-step explanation:

f(x)=2x+1 n g(x)=2x^2+1,

at x=0, f(0)=1=g(0)

x=1, f(1)=3=g(1)

in general a straight line like f(x) and a parabola like g(x) will intersect at most 2 times. in this case, at x=0 n 1.

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

f(x)<>g(x) at x=3

taylor's answer is correct for x=0 n x=1 but incorrect for x=3

Step-by-step explanation:

Given the two functions, f(x)=2x+1 and g(x)=2x^2+1,

we can calculate that for x=0,

f(0)=2(0)+1=1

g(0)=2(0)^2+1=1

f(0)=g(0)

for  x=1,

f(1)=2(1)+1=3

g(1)=2(1)^2+1=3

f(1)=g(1)

for x=3,

f(3)=2(3)+1=7

g(3)=2(3)^2+1=19

So f(x) and g(x) are different at x=3.

Taylor was incorrect at x=3.

Step-by-step explanation:

Here's why when we plug in the values of x we get:

1.f(x)=1, g(x)=1(x=0)

2.f(x)=3,g(x)=3(x=1)

3.f(x)=7,g(x)=19(x=3)

As you can see she was wrong on x=3.

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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)

Step-by-step 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