Question

Taylor graphs the following in Desmos and decides that f(x) = g(x) at x = 0, x = 1, & x = 3.

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

Provide Taylor some feedback that explains which part of the answer was incorrect and why.

Answer 1

f(x) = g(x) at x=0 and x=1. The value of f(1)=g(1) is 3.

At x=3, the function values are somewhat different.

Explanation:

The points of intersection of the two functions are (0, 1) and (1, 3). One needs to pay attention to the question being asked and how these points relate to the answer.

Generally, when we're solving f(x)=g(x), we're only concerned with the values of x that make the equation true. When you graph both f(x) and g(x) and look for points of intersection, you also find the "y" values at which the equation is true. (If you graph f(x)-g(x) and look only for x-intercepts, there is no such issue.)