Question

1)The graph of the function y = 4x does not pass through the origin.

Which two of the following statements are valid explanations for this?

Select one or more:

4x is always greater than or equal to 1

4x is never zero

When y=0, x=0

When x=0, y=4

4x is zero when x=0

When x=0, y≠0

Answer 1

The correct options are:

Option B)
`4^x` is never zero.

Option F) When x=0, y≠0

Explanation:

Consider the provided function.

`y=4^x`

When we substitute x=0 in above function we get:

`y=4^(0)`

`y=1`

When we substitute x=-1 in above function we get:

`y=4^(-1)`

`y=0.25`

When we substitute x=1 in above function we get:

`y=4^(1)`

`y=4`

The above function is exponential function which does not pass through the origin and the range of the function is a positive number.

The graph of the function is shown in figure 1.

Now consider the provided options.

Option A)
`4^x` is always greater than or equal to 1.

The option is incorrect as the value of the function is less than 1 for negative value of x.

Option B)
`4^x` is never zero

The option is correct.

Option C) When y=0, x=0

The option is incorrect.

Option D) When x=0, y=4

When x=0 the value of y is 1.

Thus, the option is incorrect.

Option E)
`4^x` is zero when x=0

When x=0 the value of
`4^x` is 1.

Thus, the option is incorrect.

Option F) When x=0, y≠0

The option is correct as 0≠1.