Given the functi is the point (-1, 4) on the graph of f?
-$$f ( x ) = \frac { x ^ { 2 } + 2 } { x + 6 }$$ Given the functi , list the x-intercepts, if any, of the graph of f.
A) (-6, 0)
B) (- 2, 0)
C) (2, 0), (-2, 0)
D) none

Question

Quizplus · Accepted Answer

BTo determine if the point (-1, 4) is on the graph of $f(x) = \frac{x^2 + 2}{x + 6}$, substitute $x = -1$ into the function and see if the output is 4. Substituting, we get $f(-1) = \frac{(-1)^2 + 2}{-1 + 6} = \frac{3}{5}$, which is not equal to 4. Therefore, the point (-1, 4) is not on the graph.For the x-intercepts, set $f(x) = 0$ and solve for $x$. This gives us the equation $\frac{x^2 + 2}{x + 6} = 0$. The numerator $x^2 + 2 = 0$ has no real solutions since $x^2 = -2$ is not possible with real numbers. Therefore, there are no x-intercepts, which corresponds to choice D for the second question. However, the explanation provided was for the first question, which was not asked. The correct explanation for the x-intercepts is that since the equation derived from setting the function equal to zero does not yield real solutions, there are no x-intercepts, confirming choice D as correct.

Given the Functi Is the Point (-1, 4) on the Graph