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

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

Answer 2

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.