Question

Can you please help me with 24Find the x and y-intercepts

Answer 1

ANSWER

• x-intercepts: (-√47, 0), and ,(√47, 0)

,

• y-intercept: (0, -47/6)

EXPLANATION

The y-intercept is the point where the graph of the function intersects the y-axis, so the x-coordinate is 0. To find the y-coordinate, we have to find f(0),

$f(0)=\frac{94-2\cdot0^2}{3\cdot0^2-12}=\frac{94-0}{0-12}=\frac{94}{-12}$

Simplify the fraction,

$f(0)=-\frac{47}{6}$

Hence, the y-intercept is (0, -47/6).

The x-intercepts are the values of x where the function is 0. To find them, we have to solve f(x) = 0. In the case of rational functions, the zeros are all the zeros of the numerator that are not zeros of the denominator,

$0=94-2x^2$

To solve this, add 2x² to both sides of the equation,

$2x^2=94$

Divide both sides by 2,

$\begin{gathered} \frac{2x^2}{2}=\frac{94}{2} \\ \\ x^2=47 \end{gathered}$

And take the square root of both sides,

$x=\pm\sqrt[]{47}$

Hence, the two x-intercepts are (-√47, 0) and (√47, 0).