Answer:
• x-intercept: (-1.5, 0).
,• y-intercept: (0, 1).
Explanation:
Given the function:
[tex]f(x)=\frac{2x+3}{x^2+3}[/tex](a)x-intercept
The x-intercept is the value of x at which f(x)=0.
When f(x)=0
[tex]\begin{gathered} \frac{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} \\ \frac{2x}{2}=-\frac{3}{2} \\ x=-1.5 \end{gathered}[/tex]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
[tex]\begin{gathered} f(x)=\frac{2x+3}{x^2+3} \\ f(x)=\frac{3}{3} \\ f(x)=1 \end{gathered}[/tex]The y-intercept is at (0, 1).
(c)Graph
The graph of f(x) is given below:
