Question

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

Answer 1

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

,

• y-intercept: (0, -47/6)

Step-by-step 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)=(94-2\cdot0^2)/(3\cdot0^2-12)=(94-0)/(0-12)=(94)/(-12)`

Simplify the fraction,

`f(0)=-(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} (2x^2)/(2)=(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).