To solve the equation \( 10 - x^2 = x + 4 \) by graphing, we can rewrite this equation as two separate functions:
- \( g(x) = x + 4 \)
- \( f(x) = 10 - x^2 \)
Now, we want to find the intersection points of these two functions, which are the solutions to the equation \( 10 - x^2 = x + 4 \).
To find the points of intersection, we set \( g(x) = f(x) \):
\[ 10 - x^2 = x + 4 \]
Rearranging this gives:
\[ -x^2 - x + 10 - 4 = 0 \] \[ -x^2 - x + 6 = 0 \]
Multiplying through by -1 gives:
\[ x^2 + x - 6 = 0 \]
Now, we can factor this quadratic equation:
\[ (x + 3)(x - 2) = 0 \]
Setting each factor to zero gives the solutions:
\[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \] \[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \]
Thus, the solution set is \({-3, 2}\).
Based on the provided options, the correct response is:
g(x) = x + 4, f(x) = 10 − x², {−3, 2}