Question

2) Let () = x − 4 and () = x2 − 10. Find the solution to the equation () = () by sketching the functions. A) 2 and 3 B) −2 and 3 C) −3 and 2 D) 0, −3, and 2

Answer 1

We have been given a system of equations. $f(x)=x-4$ and $g(x)=x^2-10$. We are asked to find the solution of the equation $f(x)=g(x)$ by sketching the functions.

We can see that f(x) is a linear function in slope-intercept form. The slope of f(x) is 1 and y-intercept at point $(0,-4)$.

We can also see that g(x) is a quadratic function. The function g(x) is an upward opening parabola, whose vertex is at point $(0,-10)$.

Upon graphing both equations, we will get our required graph as shown in the attachment.

The solution of $f(x)=g(x)$ will be the x-coordinates of points, where both functions will intersect.

We can see that both functions are intersecting at $x=-2\text{ and }3$, therefore, $-2\text{ and }3$ are the solutions of  $f(x)=g(x)$ and option B is the correct choice.