Question

If f(x) = 0, what is x?

0 only
–6 only
–2, 1, or 3 only
–6, –2, 1, or 3 only

Answer 1

Third option (–2, 1, or 3) is correct.

Explanation:

The given: if
`f(x)=0`

we need to find the points on
`x`, when
`f(x)=0`

Since,
`y=f(x)`

then,

`y=0`

This means f(x) touches the x-axis

In provided graph, we can see at
`x= -2,1\; or 3` the
`y=f(x)=0`

Hence, Third option (–2, 1, or 3) is correct.

Answer 2

Answer: Third option is correct.

Explanation:

Since we have given that

if f(x)=0

if we let y=f(x)

then,

y=0,

So, that means when f(x) touches the x-axis,

According to the graph, we get that

At x= -2 f(x)=0

As xi negative in Second quadrant , and here we can see that f(x) touches the x-axis and intersect it.

At x=1, f(x)=0

At x=3, f(x)=0.

In above cases 'x' is positive, so, x lies in First quadrant, here too f(x) crosses the x-axis twice.

Hence, Third option is correct.