Question

4 choose all linear factors of the function whose graph is shown below.
a $x + 1$

Explanation:

Step1: Identify x-intercepts

The graph crosses/touches the x-axis at $x=-2$, $x=1$, and $x=4$.

Step2: Convert to linear factors

For an x-intercept $x=a$, the linear factor is $(x-a)$.

• For $x=-2$: $(x-(-2)) = x+2$
• For $x=1$: $(x-1)$
• For $x=4$: $(x-4)$

Step3: Match with given option

The provided option A is $x+1$, which does not correspond to any x-intercept. The valid linear factors are $x+2$, $x-1$, $x-4$.

Answer:

The valid linear factors are $x+2$, $x-1$, $x-4$; the option $x+1$ is not a factor.