To show how to solve the equation by graphing, create two functions and find their intersection points. What two functions can be used to solve the following equation, and what is their solution set?

Question

10−x2=x+4


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(1 point)
Responses

g(x) = x + 4, f(x) = 10+x2, {−3,2}
g(x) = x + 4, f(x) = 10+x2, {−3,2}

g(x) = x + 4, f(x) = 10+x2, {−3,1}
g(x) = x + 4, f(x) = 10+x2, {−3,1}

g(x) = x + 4, f(x) = 10−x2, {1,6}
g(x) = x + 4, f(x) = 10−x2, {1,6}

g(x) = x + 4, f(x) = 10−x2, {−3,2}
g(x) = x + 4, f(x) = 10−x2, {−3,2}

Answer 1

To solve the equation \( 10 - x^2 = x + 4 \) by graphing, we start by rewriting it in a suitable form to define two functions.

1. Rearranging the original equation: \[ 10 - x^2 = x + 4 \] This can be rearranged to: \[ 10 - x - 4 = x^2 \] or equivalently, \[ x^2 + x - 6 = 0 \]

2. Identifying the two functions: Let's define our two functions as:

   • \( f(x) = 10 - x^2 \) (the left side of the equation)
   • \( g(x) = x + 4 \) (the right side of the equation)

3. Finding intersections: We can find their intersection points by solving for when \( f(x) = g(x) \): \[ 10 - x^2 = x + 4 \] Rearranging gives: \[ x^2 + x - 6 = 0 \]

4. Factoring the quadratic: The quadratic factors to: \[ (x - 2)(x + 3) = 0 \]

5. Solutions: From this factoring, we find the solutions are: \[ x = 2 \quad \text{and} \quad x = -3 \]

Thus, the correct functions you can use to solve the given equation by graphing are:

• \( g(x) = x + 4 \)
• \( f(x) = 10 - x^2 \)

And the solution set is: \[ {-3, 2} \]

So the correct response from the provided options is: g(x) = x + 4, f(x) = 10−x^2, {−3,2}