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.