Question

function g can be represented by the expressions $x^2 - 2x - 3$ and $(x + 1)(x - 3)$. using the expressions and the graph of the function is given below, what are the x - intercepts? a (-1,0) and (3,0) b (0,-1) and (3,0) c (1,0) and (-3,0)

Explanation:

Step1: Recall x-intercept definition

x-intercepts occur where \( y = 0 \), so solve \( g(x)=0 \).

Step2: Use factored form

Function \( g(x)=(x + 1)(x - 3) \). Set \( (x + 1)(x - 3)=0 \).

Step3: Solve for x

By zero - product property, \( x+1 = 0\) or \( x - 3=0 \). So \( x=-1 \) or \( x = 3 \). Thus, x - intercepts are \((-1,0)\) and \((3,0)\).

Answer:

A. (-1,0) and (3,0)