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

Answer:

The correct options are:

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

Option F) When x=0, y≠0

Step-by-step 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.