Question

Find the x-intercept and y- intercept of the function f(x) = (2x + 3)/(x ^ 2 + 3)can u draw the function of f(x) = (2x + 3)/(x ^ 2 + 3)?Need solution ^^

Answer 1

• x-intercept: (-1.5, 0).

,

• y-intercept: (0, 1).

Explanation:

Given the function:

`f(x)=(2x+3)/(x^2+3)`

(a)x-intercept

The x-intercept is the value of x at which f(x)=0.

When f(x)=0

`\begin{gathered} (2x+3)/(x^2+3)=0 \\ \text{ Cross multiply} \\ 2x+3=0 \\ \text{ Subtract 3 from both sides of the equation} \\ 2x+3-3=0-3 \\ 2x=-3 \\ \text{ Divide both sides of the equation by 2} \\ (2x)/(2)=-(3)/(2) \\ x=-1.5 \end{gathered}`

The x-intercept is located at (-1.5, 0).

(b)y-intercept

The y-intercept is the value of f(x) at which x=0.

When x=0

`\begin{gathered} f(x)=(2x+3)/(x^2+3) \\ f(x)=(3)/(3) \\ f(x)=1 \end{gathered}`

The y-intercept is at (0, 1).

(c)Graph

The graph of f(x) is given below: